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Marcus M. — Finite dimensional multilinear algebra. Part I
Marcus M. — Finite dimensional multilinear algebra. Part I

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Название: Finite dimensional multilinear algebra. Part I

Автор: Marcus M.

Аннотация:

This monograph covers multilinear algebra over finite dimensional vector spaces. The underlying field is always assumed to have characteristic 0.
Multilinear algebra has important intersections with many branches of pure and applied mathematics: differential geometry, algebraic geometry, invariant theory, group representation theory, partial differential equations, quantum mechanics, theory of inequalities. We assume as preparation only a rather modest background in linear algebra and general algebra that can be found in any respectable undergraduate course, e.g.


Язык: ru

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1973

Количество страниц: 292

Добавлена в каталог: 07.06.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$H \subset {S}_{m}$ acts on a set X      91
$\mathfrak{A}$ is generated by X      161
$\phi$ is homogeneous of degree k      163
${m}^{th}$ completely symmetric space over V      132
${m}^{th}$ compound of T      117
${m}^{th}$ elementary symmetry function of ${\lambda}_{1},...,{\lambda}_{n}$      129
${m}^{th}$ exterior power of T      117
${m}^{th}$ exterior space over V      131
${m}^{th}$ Grassmann space over V      131
${m}^{th}$ induced power of T      117
${m}^{th}$ skew-symmetric space      131
${m}^{th}$ tensor power of T      117
${\delta}_{g}$ derivations      212
Adjugate of an n-square matrix A      130
Algebra      160
Algebra homomorphism      161
Alternating group      94
Basis      161
Bisymmetric transformation      245
Canonical injection      11
Canonical isomorphism between V and V**      8
Canonical projection      12
Cartan's Lemma      152
Cartesian product      1
Cauchy-Binet formula      103
Cauchy-Binet theorem for generalized matrix functions      131
Cauchy-Binet theorem for permanents      109
Character of degree 1      77
Conjugate dual      70
Contraction of tensors      40
Contravariant tensor algebra      175
Contravariant tensors      36
Covariant tensor algebra      175
Covariant tensors      36
Cramers rule      188
Decomposable      19
Decomposable element of ${V}_{\chi}^{m}(H)$      91
Derivation induced by A on ${T}_{O}(V)$      210
Derivations      209
Derived algebra      161
Direct sum      63
Division algebra      160
Doubly stochastic      207
Dual      7
Dual basis      7
Dual of S      53
Dual product space      32
Dual space      2
Exterior algebra over V      178
Fischer Inequality      135
Free spaces, factor spaces, tensor products      10
Free vector space      10
G-graded algebra      162
G-graded vector space      162
Generalized matrix function      124
Generating set      161
Graded symmetric algebra over V      182
Grassmann algebra over V      178
Hadamard determinant theorem      135
Homogeneous ideal      163
Homogeneous linear transformation      163
Homogeneous of degree g      163
Homogeneous polynomial representation of degree m      257
Homogeneous sub space      163
Ideal      160
Identity matrix      55
Identity preserving      161
Induced matrix defined by A      126
Induced transformation      116
Invariant subspace      63
Iversen's linear determinant      276
Jacobi's theorem      130
Kronecker product      3
Laplace expansion theorem      189
Left ideal      160
Linear closure      6
Linearly dependent      23
Linearly independent      5
Main involution      209
Matrix representation of T      38
Mixed graded tensor algebra over V      169
Multilinear functions      1
Multiplication operator      258
Nilpotent      65
Orbits      92
Partial derivation      2Zh
Partition      222
Partition polynomial      231
Permanent      2
Permutation operator      72
Pfaffian of A      280
Polynomial algebra      187
Product of linear functionals      7
Quotient map      12
Quotient or factor space      12
Range of $\phi$      9
Rank of T      36
Restriction of T to W      63
Right ideal      160
Sesquilinear functional      44
Skew-symmetric algebra over V      178
Space of mixed tensors over V      169
Stabilizer      92
Star product      91
Star product of ${T}_{1},...,{T}_{n}$      269
Subalgebra      160
Sum of subspaces      23
Sylvester-Franke theorem      130
Symmetric "with respect to H and $\chi$      87
Symmetric multilinear function      87
Symmetric product      132
Symmetrized product      266
Symmetrizer      77
Symmetrizer defined by H and $\chi$      78
Symmetry class of tensors      88
System of distinct repres entat ives      92
Tensor multiplication      171
Tensor product      14
Tensor product of linear transformations      52
Tensors      19
Total matrix algebra      161
Triangular basis      67
Two-sided ideal      160
Universal factorization property      183
Universal tensor algebra property      183
Van der Waerden conjecture      109
Weyl's principle of the irrelevance of algebraic inequalities      256
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