Algebra / Roger Godement.
Idioma: Inglés Lenguaje original: Francés Editor: Paris : Boston : Hermann ; Houghton Mifflin, c1968Descripción: 638 p. ; 23 cmTítulos uniformes: Cours d'algèbre. Inglés Otra clasificación: 00A05 (13-01 15-01 16-01 20-01)PREFACE [15] PART I: SET THEORY [19] § 0. Logical reasoning [20] 1. The concept of logical perfection [20] 2. The real language of mathematics [22] 3. Elementary logical operations [24] 4. Axioms and theorems [25] 5. Logical axioms and tautologies [26] 6. Substitution in a relation [30] 7. Quantifiers [31] 8. Rules for quantifiers [32] 9. The Hilbert operation. Criteria of formation [35] Exercises on § 0 [38] § 1. The relations of equality and membership [41] 1. The relation of equality [41] 2. The relation of membership [42] 3. Subsets of a set [43] 4. The empty set [45] 5. Sets of one and two elements [46] 6. The set of subsets of a given set [47] Exercises on § 1 [49] § 2. The notion of a function [50] 1. Ordered pairs [50] 2. The Cartesian product of two sets [51] 3. Graphs and functions [53] 4. Direct and inverse images [56] 5. Restrictions and extensions of functions [57] 6. Composition of mappings [58] 7. Injective mappings [61] 8. Surjective and bijective mappings [62] 9. Functions of several variables [65] Exercises on § 2 [68] § 3. Unions and intersections. [70] 1. The union and intersection of two sets [70] 2. The union of a family of sets [71] 3. The intersection of a family of sets [72] Exercises on § 3 [75] §4. Equivalence relations [77] 1. Equivalence relations [77] 2. Quotient of a set by an equivalence relation [79] 3. Functions defined on a quotient set [82] Exercises on § 4 [86] § 5. Finite sets and integers [88] 1. Equipotent sets [88] 2. The cardinal of a set [89] 3. Operations on cardinals [92] 4. Finite sets and natural numbers [95] 5. The set N of the natural numbers [96] 6. Mathematical induction [98] 7. Combinatorial analysis [99] 8. The rational integers [102] 9. The rational numbers [107] Exercises on § 5 [108] PART n: GROUPS, RINGS, HELDS [113] §6. Laws of composition [114] 1. Laws of composition; associativity and commutativity [114] 2. Reflexible elements [117] § 7. Groups [120] 1. Definition of a group. Examples [120] 2. Direct product of groups [122] 3. Subgroups of a group [124] 4. The intersection of subgroups. Generators [127] 5. Permutations and transpositions [129] 6. Cosets [130] 7. The number of permutations of n objects [133] 8. Homomorphisms [134] 9. The kernel and image of a homomorphism [136] 10. Application to cyclic groups [138] 11. Groups operating on a set [139] Exercises on § 7 [142] §8. Rings and fields [148] 1. Definition of a ring. Examples [148] 2. Integral domains and fields [151] 3. Hie ring of integers modulo p [153] 4. The binomial theorem [154] 5. Expansion of a product of sums [157] 6. Ring homomorphisms [158] Exercises on § [160] §9. Complex numbers [168] 1. Square roots [168] 2. Preliminaries [168] 3. The ring K[√d] [169] 4. Units in a quadratic extension [172] 5. The case of a field [174] 6. Geometrical representation of complex numbers [175] 7. Multiplication formulae for trigonometric functions [178] Exercises on §9 [181] PART Hi: MODULES OVER A RING [187] §10. Modules and vector spaces [188] 1. Definition of a module over a ring [188] 2. Examples of modules [189] 3. Submodules; vector subspaces [191] 4. Right modules and left modules [192] §11. Linear relations in a module [194] 1. Linear combinations [194] 2. Finitely generated modules [196] 3. Linear relations [196] 4. Free modules. Bases [198] 5. Infinite linear combinations [201] Exercises on §§ 10 and 11 [203] § 12. Linear mappings. Matrices [208] 1. Homomorphisms [208] 2. Homomorphisms of a finitely generated free module into an arbitrary module [210] 3. Homomorphisms and matrices [212] 4. Examples of homomorphisms and matrices [215] §13. Addition of homomorphisms and matrices [220] 1. The additive group Hom (L, M) [220] 2. Addition of matrices [221] §14. Products of matrices [223] 1. The ring of endomorphisms of a module [223] 2. The product of two matrices [224] 3. Rings of matrices [226] 4. Matrix notation for homomorphisms [228] Exercises on §§12, 13 and 14 [230] §15. Invertible matrices and change of basis [235] 1. The group of automorphisms of a module [235] 2. The groups GL(n, K) [235] 3. Examples: the groups GL(1, K) and GL(2, K) [236] 4. Change of basis. Transition matrices [238] 5. Effect of change of bases on the matrix of a homomorphism [241] Exercises on § 15 [244] § 16. The transpose of a linear mapping [249] 1. The dual of a module [249] 2. The dual of a finitely generated free module [250] 3. The bidual of a module [252] 4. The transpose of a homomorphism [254] 5. The transpose of a matrix [255] Exercises on § 16 [259] §17. Sums of submodules [261] 1. The sum of two submodules [261] 2. Direct product of modules [262] 3. Direct sum of submodules [263] 4. Direct sums and projections [265] Exercises on §17 [268]
PART IV: FINITE-DIMENSIONAL VECTOR SPACES [271] §18. Finiteness theorems [272] 1. Homomorphisms whose kernel and image are finitely generated [272] 2. Finitely generated modules over a Noetherian ring [273] 3. Submodules of a free module over a principal ideal domain [274] 4. Applications to systems of linear equations [275] 5. Other characterizations of Noetherian rings [277] Exercises on § 18 [279] § 19. Dimension [282] 1. Existence of bases [282] 2. Definition of a vector subspace by means of linear equations [284] 3. Conditions for consistency of a system of linear equations [285] 4. Existence of linear relations [287] 5. Dimension [289] 6. Characterizations of bases and dimension [291] 7. Dimensions of the kernel and image of a homomorphism [292] 8. Rank of a homomorphism; rank of a family of vectors; rank of a matrix [294] 9. Computation of the rank of a matrix [295] 10. Calculation of the dimension of a vector subspace from its equations [298] Exercises on § 19 [300] § 20. Linear equations [306] 1. Notation and terminology [306] 2. The rank of a system of linear equations. Conditions for the existence of solutions [307] 3. The associated homogeneous system [308] 4. Cramer systems [308] 5. Systems of independent equations: reduction to a Cramer system [310] Exercises on § 20 [313] PART V: DETERMINANTS [317] §21. Multilinear functions [318] 1. Definition of multilinear mappings [318] 2. The tensor product of multilinear mappings [321] 3. Some algebraic identities [323] 4. The case of finitely generated free modules [326] 5. The effect of a change of basis on the components of a tensor [333] Exercises on § 21 [336] § 22. Alternating bilinear mappings [341] 1. Alternating bilinear mappings [341] 2. The case of finitely generated free modules [342] 3. Alternating trilinear mappings [345] 4. Expansion with respect to a basis [346] Exercises on §22 [350] § 23. Alternating multilinear mappings [353] 1. The signature of a permutation [353] 2. Antisymmetrization of a function of several variables [357] 3. Alternating multilinear mappings [359] 4. Alternating p-linear functions on a module isomorphic to Kp [361] 5. Determinants [362] 6. Characterization of bases of a finite-dimensional vector space [366] 7. Alternating multilinear mappings: the general case [369] 8. The criterion for linear independence [371] 9. Conditions for consistency of a system of linear equations [373] Exercises on § 23 [376] § 24. Determinants [380] 1. Fundamental properties of determinants [380] 2. Expansion of a determinant along a row or column [382] 3. The adjugate matrix [386] 4. Cramer’s formulae [387] Exercises on §24 [390] § 25. Affine spaces [396] 1. The vector space of translations [396] 2. Affine spaces associated with a vector space [397] 3. Barycentres in an affine space [399] 4. Linear varieties in an affine space [402] 5. Generation of a linear variety by means of lines [405] 6. Finite-dimensional affine spaces. Affine bases [406] 7. Calculation of the dimension of a linear variety [408] 8. Equations of a linear variety in affine coordinates [410] PART VI: POLYNOMIALS AND ALGEBRAIC EQUATIONS [413] § 26. Algebraic relations [414] 1. Monomials and polynomials in the elements of a ring [414] 2. Algebraic relations [416] 3. The case of fields [417] Exercises on § 26 [420] Polynomial rings [423] I. Preliminaries on the case of one variable [423] X Polynomials in one indeterminate [423] 3-Polynomial notation [426] 4. Polynomials in several indeterminates [428] 5, Partial and total degrees [429] 4. Polynomials with coefficients in an integral domain [430] 5 28 Polynomial functions [432] 1. The values of a polynomial [432] 2. The sum and product of polynomial functions [433] 3- The case of an infinite field [435] Exercises on 27 and 28 [438] f 24- Rational fractions [446] I, The field of fractions of an integral domain: preliminaries [446] X Contruction of the field of fractions [447] 3. Verification of the field axioms [450] 4. Embedding the ring K in its field of fractions [451] 5. Rational fractions with coefficients in a field [452] 6. Values of a rational fraction [454] Exercises on 29 [458] 130. Derivations. Taylor’s formula [463] 1. Derivations of a ring. [463] X Derivations of a polynomial ring [464] X Partial derivatives [466] 4, Derivation of composite functions [467] X Taylor’s formula [468] 6. The characteristic of a field [470] 7. Multiplicities of the roots of an equation [471] Exercises on § 30 [475] f 31, Principal ideal domains [479] 1. Highest common factor [479] 2. Coprime elements [480] 3. Least common multiple [481] 4. Existence of prime divisors [482] 5. Properties of extremal elements [484] 6. Uniqueness of the decomposition into prime factors [485] 7. Calculation of h.c.f. and l.c.m. by means of prime factorization [486] 8. Decomposition into partial fractions over a principal ideal domain [488] Exercises on § 31 [491] § 32. Division of polynomials [497] 1. Division of polynomials in one variable [497] 2. Ideals in a polynomial ring in one indeterminate [500] 3. The h.c.f. and l.c.m. of several polynomials. Irreducible polynomials [501] 4. Application to rational fractions [503] Exercises on § 32 [506] §33. The roots of an algebraic equation [515] 1. The maximum number of roots [515] 2. Algebraically closed fields [517] 3. Number of roots of an equation with coefficients in an algebraically closed field [519] 4. Irreducible polynomials with coefficients in an algebraically closed field [521] 5. Irreducible polynomials with real coefficients [522] 6. Relations between the coefficients and the roots of an equation [524] Exercises on § 33 [526] PART VII: REDUCTION OF MATRICES [537] § 34. Eigenvalues [538] 1. Definition of eigenvectors and eigenvalues [538] 2. The characteristic polynomial of a matrix [539] 3. The form of the characteristic polynomial [540] 4. The existence of eigenvalues [541] 5. Reduction to triangular form [541] 6. The case in which all the eigenvalues are simple [545] 7. Characterization of diagonalizable endomorphisms [548] Exercises on § 34 [551] § 35. The canonical form of a matrix [565] 1. The Cayley-Hamilton theorem [565] 2. Decomposition into nilpotent endomorphisms [567] 3. The structure of nilpotent endomorphisms [569] 4. Jordan’s theorem [572] Exercises on § 35 [575] § 36. Hermitian forms [583] 1. Sesquilinear forms; hermitian forms [583] 2. Non-degenerate forms [586] 3. The adjoint of a homomorphism [588] 4. Orthogonality with respect to a non-degenerate hermitian form [591] 5. Orthogonal bases [596] 6. Orthonormal bases [598] 7. Automorphisms of a hermitian form [600] 8. Automorphisms of a positive definite hermitian form. Reduction to diagonal form [602] 9. Isotropic vectors and indefinite forms [606] 10. The Cauchy-Schwarz inequality [607] Exercises on § 36 [610] BIBLIOGRAPHY INDEX OF NOTATION [626] INDEX OF TERMINOLOGY
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|---|
Libros
|
Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A05A G581i (Browse shelf) | Available | A-3988 |
Browsing Instituto de Matemática, CONICET-UNS shelves, Shelving location: Libros ordenados por tema Close shelf browser
| 00A05A D554 Algebraic theories : | 00A05A D889-3 Abstract algebra / | 00A05A G581-2 Cours d'algèbre / | 00A05A G581i Algebra / | 00A05A H572a Álgebra abstracta / | 00A05A H572a Álgebra abstracta / | 00A05A H572t Topics in algebra / |
Traducción de: Cours d'algèbre. Paris : Hermann, 1963.
"Based on lecture-courses given by the author at the University of Paris."
Bibliografía: p. [622]-625.
PREFACE [15] --
PART I: SET THEORY [19] --
§ 0. Logical reasoning [20] --
1. The concept of logical perfection [20] --
2. The real language of mathematics [22] --
3. Elementary logical operations [24] --
4. Axioms and theorems [25] --
5. Logical axioms and tautologies [26] --
6. Substitution in a relation [30] --
7. Quantifiers [31] --
8. Rules for quantifiers [32] --
9. The Hilbert operation. Criteria of formation [35] --
Exercises on § 0 [38] --
§ 1. The relations of equality and membership [41] --
1. The relation of equality [41] --
2. The relation of membership [42] --
3. Subsets of a set [43] --
4. The empty set [45] --
5. Sets of one and two elements [46] --
6. The set of subsets of a given set [47] --
Exercises on § 1 [49] --
§ 2. The notion of a function [50] --
1. Ordered pairs [50] --
2. The Cartesian product of two sets [51] --
3. Graphs and functions [53] --
4. Direct and inverse images [56] --
5. Restrictions and extensions of functions [57] --
6. Composition of mappings [58] --
7. Injective mappings [61] --
8. Surjective and bijective mappings [62] --
9. Functions of several variables [65] --
Exercises on § 2 [68] --
§ 3. Unions and intersections. [70] --
1. The union and intersection of two sets [70] --
2. The union of a family of sets [71] --
3. The intersection of a family of sets [72] --
Exercises on § 3 [75] --
§4. Equivalence relations [77] --
1. Equivalence relations [77] --
2. Quotient of a set by an equivalence relation [79] --
3. Functions defined on a quotient set [82] --
Exercises on § 4 [86] --
§ 5. Finite sets and integers [88] --
1. Equipotent sets [88] --
2. The cardinal of a set [89] --
3. Operations on cardinals [92] --
4. Finite sets and natural numbers [95] --
5. The set N of the natural numbers [96] --
6. Mathematical induction [98] --
7. Combinatorial analysis [99] --
8. The rational integers [102] --
9. The rational numbers [107] --
Exercises on § 5 [108] --
PART n: GROUPS, RINGS, HELDS [113] --
§6. Laws of composition [114] --
1. Laws of composition; associativity and commutativity [114] --
2. Reflexible elements [117] --
§ 7. Groups [120] --
1. Definition of a group. Examples [120] --
2. Direct product of groups [122] --
3. Subgroups of a group [124] --
4. The intersection of subgroups. Generators [127] --
5. Permutations and transpositions [129] --
6. Cosets [130] --
7. The number of permutations of n objects [133] --
8. Homomorphisms [134] --
9. The kernel and image of a homomorphism [136] --
10. Application to cyclic groups [138] --
11. Groups operating on a set [139] --
Exercises on § 7 [142] --
§8. Rings and fields [148] --
1. Definition of a ring. Examples [148] --
2. Integral domains and fields [151] --
3. Hie ring of integers modulo p [153] --
4. The binomial theorem [154] --
5. Expansion of a product of sums [157] --
6. Ring homomorphisms [158] --
Exercises on § [160] --
§9. Complex numbers [168] --
1. Square roots [168] --
2. Preliminaries [168] --
3. The ring K[√d] [169] --
4. Units in a quadratic extension [172] --
5. The case of a field [174] --
6. Geometrical representation of complex numbers [175] --
7. Multiplication formulae for trigonometric functions [178] --
Exercises on §9 [181] --
PART Hi: MODULES OVER A RING [187] --
§10. Modules and vector spaces [188] --
1. Definition of a module over a ring [188] --
2. Examples of modules [189] --
3. Submodules; vector subspaces [191] --
4. Right modules and left modules [192] --
§11. Linear relations in a module [194] --
1. Linear combinations [194] --
2. Finitely generated modules [196] --
3. Linear relations [196] --
4. Free modules. Bases [198] --
5. Infinite linear combinations [201] --
Exercises on §§ 10 and 11 [203] --
§ 12. Linear mappings. Matrices [208] --
1. Homomorphisms [208] --
2. Homomorphisms of a finitely generated free module into an arbitrary module [210] --
3. Homomorphisms and matrices [212] --
4. Examples of homomorphisms and matrices [215] --
§13. Addition of homomorphisms and matrices [220] --
1. The additive group Hom (L, M) [220] --
2. Addition of matrices [221] --
§14. Products of matrices [223] --
1. The ring of endomorphisms of a module [223] --
2. The product of two matrices [224] --
3. Rings of matrices [226] --
4. Matrix notation for homomorphisms [228] --
Exercises on §§12, 13 and 14 [230] --
§15. Invertible matrices and change of basis [235] --
1. The group of automorphisms of a module [235] --
2. The groups GL(n, K) [235] --
3. Examples: the groups GL(1, K) and GL(2, K) [236] --
4. Change of basis. Transition matrices [238] --
5. Effect of change of bases on the matrix of a homomorphism [241] --
Exercises on § 15 [244] --
§ 16. The transpose of a linear mapping [249] --
1. The dual of a module [249] --
2. The dual of a finitely generated free module [250] --
3. The bidual of a module [252] --
4. The transpose of a homomorphism [254] --
5. The transpose of a matrix [255] --
Exercises on § 16 [259] --
§17. Sums of submodules [261] --
1. The sum of two submodules [261] --
2. Direct product of modules [262] --
3. Direct sum of submodules [263] --
4. Direct sums and projections [265] --
Exercises on §17 [268] --
PART IV: FINITE-DIMENSIONAL VECTOR SPACES [271] --
§18. Finiteness theorems [272] --
1. Homomorphisms whose kernel and image are finitely generated [272] --
2. Finitely generated modules over a Noetherian ring [273] --
3. Submodules of a free module over a principal ideal domain [274] --
4. Applications to systems of linear equations [275] --
5. Other characterizations of Noetherian rings [277] --
Exercises on § 18 [279] --
§ 19. Dimension [282] --
1. Existence of bases [282] --
2. Definition of a vector subspace by means of linear equations [284] --
3. Conditions for consistency of a system of linear equations [285] --
4. Existence of linear relations [287] --
5. Dimension [289] --
6. Characterizations of bases and dimension [291] --
7. Dimensions of the kernel and image of a homomorphism [292] --
8. Rank of a homomorphism; rank of a family of vectors; rank of a matrix [294] --
9. Computation of the rank of a matrix [295] --
10. Calculation of the dimension of a vector subspace from its equations [298] --
Exercises on § 19 [300] --
§ 20. Linear equations [306] --
1. Notation and terminology [306] --
2. The rank of a system of linear equations. Conditions for the existence of solutions [307] --
3. The associated homogeneous system [308] --
4. Cramer systems [308] --
5. Systems of independent equations: reduction to a Cramer system [310] --
Exercises on § 20 [313] --
PART V: DETERMINANTS [317] --
§21. Multilinear functions [318] --
1. Definition of multilinear mappings [318] --
2. The tensor product of multilinear mappings [321] --
3. Some algebraic identities [323] --
4. The case of finitely generated free modules [326] --
5. The effect of a change of basis on the components of a tensor [333] --
Exercises on § 21 [336] --
§ 22. Alternating bilinear mappings [341] --
1. Alternating bilinear mappings [341] --
2. The case of finitely generated free modules [342] --
3. Alternating trilinear mappings [345] --
4. Expansion with respect to a basis [346] --
Exercises on §22 [350] --
§ 23. Alternating multilinear mappings [353] --
1. The signature of a permutation [353] --
2. Antisymmetrization of a function of several variables [357] --
3. Alternating multilinear mappings [359] --
4. Alternating p-linear functions on a module isomorphic to Kp [361] --
5. Determinants [362] --
6. Characterization of bases of a finite-dimensional vector space [366] --
7. Alternating multilinear mappings: the general case [369] --
8. The criterion for linear independence [371] --
9. Conditions for consistency of a system of linear equations [373] --
Exercises on § 23 [376] --
§ 24. Determinants [380] --
1. Fundamental properties of determinants [380] --
2. Expansion of a determinant along a row or column [382] --
3. The adjugate matrix [386] --
4. Cramer’s formulae [387] --
Exercises on §24 [390] --
§ 25. Affine spaces [396] --
1. The vector space of translations [396] --
2. Affine spaces associated with a vector space [397] --
3. Barycentres in an affine space [399] --
4. Linear varieties in an affine space [402] --
5. Generation of a linear variety by means of lines [405] --
6. Finite-dimensional affine spaces. Affine bases [406] --
7. Calculation of the dimension of a linear variety [408] --
8. Equations of a linear variety in affine coordinates [410] --
PART VI: POLYNOMIALS AND ALGEBRAIC EQUATIONS [413] --
§ 26. Algebraic relations [414] --
1. Monomials and polynomials in the elements of a ring [414] --
2. Algebraic relations [416] --
3. The case of fields [417] --
Exercises on § 26 [420] --
Polynomial rings [423] --
I. Preliminaries on the case of one variable [423] --
X Polynomials in one indeterminate [423] --
3-Polynomial notation [426] --
4. Polynomials in several indeterminates [428] --
5, Partial and total degrees [429] --
4. Polynomials with coefficients in an integral domain [430] --
5 28 Polynomial functions [432] --
1. The values of a polynomial [432] --
2. The sum and product of polynomial functions [433] --
3- The case of an infinite field [435] --
Exercises on 27 and 28 [438] --
f 24- Rational fractions [446] --
I, The field of fractions of an integral domain: preliminaries [446] --
X Contruction of the field of fractions [447] --
3. Verification of the field axioms [450] --
4. Embedding the ring K in its field of fractions [451] --
5. Rational fractions with coefficients in a field [452] --
6. Values of a rational fraction [454] --
Exercises on 29 [458] --
130. Derivations. Taylor’s formula [463] --
1. Derivations of a ring. [463] --
X Derivations of a polynomial ring [464] --
X Partial derivatives [466] --
4, Derivation of composite functions [467] --
X Taylor’s formula [468] --
6. The characteristic of a field [470] --
7. Multiplicities of the roots of an equation [471] --
Exercises on § 30 [475] --
f 31, Principal ideal domains [479] --
1. Highest common factor [479] --
2. Coprime elements [480] --
3. Least common multiple [481] --
4. Existence of prime divisors [482] --
5. Properties of extremal elements [484] --
6. Uniqueness of the decomposition into prime factors [485] --
7. Calculation of h.c.f. and l.c.m. by means of prime factorization [486] --
8. Decomposition into partial fractions over a principal ideal domain [488] --
Exercises on § 31 [491] --
§ 32. Division of polynomials [497] --
1. Division of polynomials in one variable [497] --
2. Ideals in a polynomial ring in one indeterminate [500] --
3. The h.c.f. and l.c.m. of several polynomials. Irreducible polynomials [501] --
4. Application to rational fractions [503] --
Exercises on § 32 [506] --
§33. The roots of an algebraic equation [515] --
1. The maximum number of roots [515] --
2. Algebraically closed fields [517] --
3. Number of roots of an equation with coefficients in an algebraically closed field [519] --
4. Irreducible polynomials with coefficients in an algebraically closed field [521] --
5. Irreducible polynomials with real coefficients [522] --
6. Relations between the coefficients and the roots of an equation [524] --
Exercises on § 33 [526] --
PART VII: REDUCTION OF MATRICES [537] --
§ 34. Eigenvalues [538] --
1. Definition of eigenvectors and eigenvalues [538] --
2. The characteristic polynomial of a matrix [539] --
3. The form of the characteristic polynomial [540] --
4. The existence of eigenvalues [541] --
5. Reduction to triangular form [541] --
6. The case in which all the eigenvalues are simple [545] --
7. Characterization of diagonalizable endomorphisms [548] --
Exercises on § 34 [551] --
§ 35. The canonical form of a matrix [565] --
1. The Cayley-Hamilton theorem [565] --
2. Decomposition into nilpotent endomorphisms [567] --
3. The structure of nilpotent endomorphisms [569] --
4. Jordan’s theorem [572] --
Exercises on § 35 [575] --
§ 36. Hermitian forms [583] --
1. Sesquilinear forms; hermitian forms [583] --
2. Non-degenerate forms [586] --
3. The adjoint of a homomorphism [588] --
4. Orthogonality with respect to a non-degenerate hermitian form [591] --
5. Orthogonal bases [596] --
6. Orthonormal bases [598] --
7. Automorphisms of a hermitian form [600] --
8. Automorphisms of a positive definite hermitian form. Reduction to diagonal form [602] --
9. Isotropic vectors and indefinite forms [606] --
10. The Cauchy-Schwarz inequality [607] --
Exercises on § 36 [610] --
BIBLIOGRAPHY --
INDEX OF NOTATION [626] --
INDEX OF TERMINOLOGY --
MR, 28 #2106 (del original en francés)
Click on an image to view it in the image viewer
There are no comments on this title.