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Golan J.S. — The Linear Algebra a Beginning Graduate Student Ought to Know (Texts in the Mathematical Sciences)
Golan J.S. — The Linear Algebra a Beginning Graduate Student Ought to Know (Texts in the Mathematical Sciences)

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Название: The Linear Algebra a Beginning Graduate Student Ought to Know (Texts in the Mathematical Sciences)

Автор: Golan J.S.

Аннотация:

This is an excellent introduction to graduate-level linear algebra, touching on theory, applications, and algorithms. It's one of those books I wish had been available when I was in grad school.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd

Год издания: 2007

Количество страниц: 442

Добавлена в каталог: 19.08.2015

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Addition in a field      6
Addition, vector      17
Adjacency matrix      353
Adjoint matrix      213
Adjoint transformation      339
Affine subset      86
Affine transformation      86
Algebra      33
Algebra, anticommutative      34
Algebra, associative      33
Algebra, Cayley      302
Algebra, commutative      34
Algebra, division      45
Algebra, entire      38
Algebra, exterior      416
Algebra, Jordan      37
Algebra, Lie      35
Algebra, optimization      10
Algebra, quaternion      58
Algebra, tensor      415
Algebra, unital      33
algebraic      65
Algebraic multiplicity      244
Algebraically closed      43
Alphabet      20
angle      325
Annihilate      247
Anti-Hermitian matrix      366
Anticommutative algebra      34
Antitrace      296
Apollonius' identity      323
Arnoldi process      331
Associative algebra      33
Automorphism      101
Automorphism of algebras      101
Automorphism, elementary      102
Automorphism, unitary      369
Axiom of Choice      3
Band matrix      133
Basis      55
Basis, canonical      57 271
Basis, dual      290
Basis, Hamel      61
Bernstein function      94
Bessel's identity      336
Best approximation      395
Bijective      2
Bilinear form      401
Bilinear form, nondegenerate      401
Bilinear transformation      399
Bilinear transformation, symmetric      399
Binet — Cauchy identity      322
Binomial formula      16
block form      123
Bounded      60 307
Bounded support      347
Bra-ket product      121
Brauer's theorem      314
Canonical basis      57 271
Cantor set      61
Cartesian product      2
Cassini oval      314
Cauchy — Schwarz — Bunyakovsky Theorem      304
Cayley algebra      302
Cayley — Hamilton theorem      250
Chain      53
Chain subset      53
Change-of-basis matrix      146
Characteristic      10
Characteristic function      21
Characteristic polynomial      239 268
Characteristic value      229
Characteristic vector      229
Chebyshev polynomial      327
Cholesky decomposition      360
Circulant matrix      156
Co-independent hyperplanes      298
Coefficient      38
Coefficient matrix      171
Coefficient, Fourier      333
Coefficient, leading      38
Coefficient, Taylor      104
Column equivalent      145
Column space      179
Combination, linear      24
Commutative algebra      34
Commuting pair      36
Companion matrix      240
Complement      68
Complement, orthogonal      330
Completely reducible      43
Complex conjugate      8
Complex number      7
Condition number      190
Condition number, spectral      383
Congruent matrices      403
Conjugate transpose      301
Conjugate, complex      8
Continuant      221
Convex subset      365
Coproduct, direct      22
Courant — Fischer minimax theorem      354
Cramer's theorem      215
Cross product      36
Crout's algorithm      153
Cyclic      104
Cyclotomic polynomial      42
Decomposition, Cholesky      360
Decomposition, direct sum      67
Decomposition, LU      153
Decomposition, polar      382
Decomposition, QR      335
Decomposition, singular value      382
Decomposition, spectral      379
Defective eigenvalue      244
Degree of a generalized eigenvector      275
Degree of a polynomial      38
Degree of a polynomial function      41
Derivation      100
Derogatory endomorphism      244
Determinant      205
Determinant function      199
Diagonal matrix      132
Diagonalizable endomorphism      236
Difference set      2
Differential      80
Differential operator      100
DIMENSION      63
Dirac functional      289
Direct coproduct      22
Direct product      19
Direct sum      66
Direct sum decomposition      67
Discrete cosine transform      137
Discrete Fourier Transform      136 308
Disjoint subspaces      23
Distance      315
distribution      286
Division algebra      45
Division algorithm      40
Domain      2
Domain, integral      10
Dot product      300
Dot product, weighted      301
Dual basis      290
Dual space      285
Dual space, weak      290
Dyadic product      130
Eigenspace      231 233
Eigenspace, generalized      276
Eigenvalue      229 232
Eigenvalue, defective      244
Eigenvalue, semisimple      244
Eigenvalue, simple      244
Eigenvector      229 232
Eigenvector, generalized      275
Eisenstein's criterion      42
Elementary automorphism      102
Elementary matrix      137
Elementary operation      143
Endomorphism      99
Endomorphism, bounded      112
Endomorphism, derogatory      244
Endomorphism, diagonalizable      236
Endomorphism, nilpotent      272
Endomorphism, normal      375
Endomorphism, orthogonally diagonalizable      352
Endomorphism, positive definite      356
Endomorphism, selfadjoint      349
Entangled tensors      410
Entire      38
EPIC      2
Epimorphism      85
Equal functions      2
Equivalence relation      106
Equivalent matrices      145
Euclidean norm      305
Euclidean subfield      299
Evaluation functional      291
Even function      69
Even permutation      203
Exchange property      26
Extended coefficient matrix      171
Exterior algebra      416
Exterior power      416
Exterior product      121
Exterior square      416
Factor space      98
Fan      168
Fast Fourier Transform      136
Fibonacci sequence      269
Field      6
Field of algebraic numbers      65
Field, algebraically closed      43
Field, formally-real      300
Field, Galois      9
Field, orderable      16
Finite dimensional      63
Finitely generated      26
Fixed point      231
Fixed space      231
Form, bilinear      401
Form, Lorentz      408
Form, quadratic      407
Formal differentiation      104
Formally real field      300
Fourier coefficient      333
Fredholm alternative      293
Frobenius norm      311
Full pivoting      152
Function      2
Function, characteristic      21
Function, determinant      199
Function, even      69
Function, inverse      2
Function, odd      69
Function, periodic      62
Function, piecewise constant      30
Function, spline      48
Functional, Dirac      289
Functional, evaluation      291
Functional, linear      285
Functional, zero      285
Fundamental theorem of algebra      43
Galois field      9
Gauss — Jordan method      175
Gauss — Seidel iteration method      186
Gaussian elimination      175
General Lie algebra      131
General quadratic equation      410
Generalized eigenspace      276
Generalized eigenvector      275
Generating set      25
Geometric multiplicity      244
Gershgorin bound      312
Gershgorin's theorem      312
Givens rotation matrix      370
GMRES algorithm      331
Golden ratio      269
Google matrix      254
Gram matrix      303
Gram — Schmidt process      328
Gram — Schmidt Theorem      328
Graph      81
Grassmann's Theorem      69
Greville's method      392
Group of automorphisms      107
Guttman's Theorem      138
Haar wavelet      332
Hadamard inequality      329
Hadamard matrix      207
Hadamard product      157
Hamel basis      61
Hamming norm      315
Hankel matrix      219
Hausdorff maximum principle      60
Hermitian matrix      351
Hermitian transpose      301
Hibert subset      332
Hilbert matrix      144
Hilbert — Schmidt norm      311
Homogeneous system of linear equations      170
Homomorphism      79
Homomorphism of algebras      79
Homomorphism of unital algebras      79
Householder matrix      373
Hyperplane      292
Ill-conditioned      189
Image      85
Imaginary part      7
Improper subspace      22
Independent subspaces      67
Indeterminate      38
Index of nilpotence      272
Induced norm      310
Infinite dimensional      63
Inner product      299
Inner product space      300
Integral domain      10
Interior product      121
Interpolation problem      169
Intersection      2
Invariant subspace      103
Inverse function      2
inversion      202
Involution      341
Irreducible      41
Isometry      362
Isomorphic vector spaces      87
Isomorphism      85
Isomorphism of algebras      85
Isomorphism of unital algebras      85
Iteration method, Gauss — Seidel      186
Iteration method, Jacobi      186
Jacobi identity      36
Jacobi iteration method      186
Jacobi overrelaxation method      188
Jacobi polynomial      327
JOR      188
Jordan algebra      37
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