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Katznelson I., KatznelsonY.R. — A (Terse) Introduction to Linear Algebra (Student Mathematical Library)
Katznelson I.,  KatznelsonY.R. — A (Terse) Introduction to Linear Algebra (Student Mathematical Library)

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Название: A (Terse) Introduction to Linear Algebra (Student Mathematical Library)

Автор: Katznelson I., KatznelsonY.R.

Аннотация:

Linear algebra is the study of vector spaces and the linear maps between them. It underlies much of modern mathematics and is widely used in applications. A (Terse) Introduction to Linear Algebra is a concise presentation of the core material of the subject — those elements of linear algebra that every mathematician, and everyone who uses mathematics, should know. It goes from the notion of a finite-dimensional vector space to the canonical forms of linear operators and their matrices, and covers along the way such key topics as: systems of linear equations, linear operators and matrices, determinants, duality, and the spectral theory of operators on inner-product spaces. The last chapter offers a selection of additional topics indicating directions in which the core material can be applied. The Appendix provides all the relevant background material. Written for students with some mathematical maturity and an interest in abstraction and formal reasoning, the book is self-contained and is appropriate for an advanced undergraduate course in linear algebra.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 224

Добавлена в каталог: 15.05.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint of a matrix      112
Adjoint of an operator      63 112
Algebra      200
Alternating form      72
Annihilator      59
Automorphism      7
Axiom of Choice      20
Basic partition      175
Basis      15
Basis, dual      58
Basis, standard      17
Bilinear form      59 63 69
Bilinear map      69
Canonical prime-power decomposition      140
Cauchy — Schwarz      105
Cayley — Hamilton      95
CHARACTER      124
Characteristic polynomial of a matrix      86
Characteristic polynomial of an operator      85
Codimension      18
Cofactor      80
Complement      11
composition      39
Congruent matrices      163
Conjugate matrices      43
Conjugate operators      40
Conjugation in $S_{n}$      67
Conjugation, group actions      196
Connecting chain      171
Contraction      132
Coset      10 192
CYCLE      65 66
Cyclic decomposition      152
Cyclic system      94
Cyclic vector      94
Decomposition, cyclic      150 152
Decomposition, general      138
Decomposition, prime power      140
Degrees of freedom      28
Determinant of a matrix      79
Determinant of an operator      76
Diagonal matrix      44
Diagonal sum      81 136
Diagonalizable      49
DIMENSION      17 18
Direct sum of subspaces      11
Direct sum, formal      10
Eigenspace      86
Eigenspace, generalized      142
Eigenvalue      64 86 89
Eigenvector      64 86 89
Eigenvector, dominant      168
Elementary divisors      155
Equivalence relation      187
Euclidean space      103
Factorization in $\mathbb{R}[x]$      206
Factorization, prime-power      140 141 204
Field      2
Field, extension      200
Fixed point      65
Flag      92
Fourier expansion      125
Frobenius      175
Gauss — Jordan elimination      26
Gaussian elimination      24
Group      1 189
Group, abelian      1
Group, cyclic      192
Group, dual      125
Group, general linear      40 43
Hadamard's inequality      110
Hamel basis      20
Hermitian form      103 163
Ideal      197
Idempotent      41 110
Independent subspaces      11 13
Independent vectors      14
Inertia, law of      165
Inner product      103
Irreducible, polynomial      203
Irreducible, system      135
Isomorphism      6
Jordan canonical form      151 156
k-form      69
Kernel      51
Lagrange      62
linear combination      9
Linear equations, homogeneous      22
Linear equations, nonhomogeneous      22
Linear operator      35
Linear system      40 49
Markov chain      178
Markov chain, reversible      179
Matrix, augmented      25
Matrix, companion      96
Matrix, derogatory      97
Matrix, diagonal      9
Matrix, hermitian      113
Matrix, integral      82
Matrix, nonderogatory      97
Matrix, nonnegative      166 170
Matrix, orthogonal      122
Matrix, permutation      44
Matrix, positive      167
Matrix, self-adjoint      113
Matrix, skew-symmetric      9
Matrix, stochastic      178
Matrix, strongly transitive      175
Matrix, symmetric      8
Matrix, transitive      171
Matrix, triangular      9 81 92
Matrix, unimodular      82
Matrix, unipotent      151
Matrix, unitary      122
Minimal polynomial      96
Minimal polynomial for $(T,\nu)$      93
Minimal system      100
Minmax principle      118
Monic polynomial      201
Multilinear form      69
Multilinear map      69
Nilpotent      147
Nilspace      142
Norm of an operator      56
Norm on a vector space      32
Normal operator      119
Nullity      51
NullSpace      52
Operator, derogatory      97
Operator, induced on a quotient      78
Operator, linear      35
Operator, nonderogatory      97
Operator, nonnegative definite      127
Operator, nonsingular      52
Operator, normal      119
Operator, orthogonal      121
Operator, positive definite      127
Operator, self-adjoint      113
Operator, singular      52
Operator, unitary      121
Order element      192
Order group      189
Orientation      77
Orthogonal equivalence      122
Orthogonal operator      121
Orthogonal projection      108
Orthogonal vectors      106
Orthonormal      106
Period group      174
periodicity      174
Permutation      65 189
Permutation matrix      44
Perron      168
Pivot column      26
Polar decomposition      128
Polarization      111
Primary components      140
Probability vector      178
Projection      41
Projection, along a subspace      36
Projection, orthogonal      108
Quadratic form      162
Quadratic form, positive definite      165
Quotient space      9
RANGE      51
Rank of a matrix      29
Rank of an operator      51
Rank, column      29
Rank, row      25
Reduced-row-echelon form      26
Reducing subspace      135
Regular representation      185
Representation      181
Representation, equivalent      182
Representation, faithful      181
Representation, reducible      184
Representation, regular      185
Representation, unitary      181
Restriction of an operator      78
Return times      171
Ring      196
Row equivalence      25
Schur decomposition      123
Schur's lemma      100
Self-adjoint algebra      117
Self-adjoint operator      113
Semisimple algebra      144
Semisimple system      142
Shift, k-shift      148
Shift, standard      148
Similar matrices      49
Similar operators      49
Singular value decomposition      131
Singular values      130
Solution-set      8 23
span      9 14
Spectral mapping theorem      89
Spectral norm      162 167
Spectral theorems      114—120
Spectrum      89 141
Spectrum of a matrix      86
Spectrum of an operator      85
Spectrum, joint      117
Square-free      143
Steinitz' lemma      17
Stochastic      178
Subalgebra      200
Subgroup, index      192
Subgroup, normal      193
SubMatrix      30
Submatrix, principal      30
Support      167
Sylvester matrix      32
Symmetric form      72
Symmetric group      65
Tensor product      12
Trace      87
Transition matrix      178
Transposition      66
Unitary dilation      132
Unitary equivalence      122
Unitary group      183
Unitary operator      121
Unitary space      103
Vandermonde      82
Vector space      4
Vector space, complex      4
Vector space, real      4
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