Marcus M., Minc H. — Introduction to Linear Algebra :: Электронная библиотека попечительского совета мехмата МГУ

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Marcus M., Minc H. — Introduction to Linear Algebra

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Название: Introduction to Linear Algebra

Авторы: Marcus M., Minc H.

Аннотация:

Rigorous, self-contained introduction at undergraduate level covers vector spaces and linear transformations, linear equations and determinants, characteristic roots. Includes 16 sets of true-false quizzes and exercises (with worked-out solutions), a complete theory of permutations and much more.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 288

Добавлена в каталог: 02.04.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$(a_{ij})$       47
$<u_{1},...,u_{k}>$       5
$A(\alpha|\beta)$       126
$A(\alpha|\beta]$       126
$A[\alpha|\beta)$       126
$A[\alpha|\beta]$       126
$A^{(j)}$       47
$A^{T}$       51
$A_{(i)}$       47
$diag(\alpha_{1},...,\alpha_{2})$       47
$d_{\chi}(A)$       119
$E^{(i)+e(j)}$       92
$E^{(i),(j)}$       92
$E^{c(i)}$       92
$E_{(i)+e(j)}$       90
$E_{(i),(j)}$       90
$E_{c(i)}$       90
$E_{ij}$       86 90
$E_{r(A)}$       149
$E_{r}(\alpha_{1},...,\alpha_{n})$       149
$e_{t}$       5
$G_{r,n}$       126
$I_{n}$       47
$I_{U}$       18
$L^{\bot}$       31
$M_{m,n}(R)$       47
$M_{n}(R)$       47
$n(\sigma)$       112
$O_{m,n}$       47
$Q_{r,n}$       126
$S_{n}$       108
$T:U \rightarrow V$       18
$V_{n}(R)$       4
$[T]G^{H}$       46
$\alpha^{'}$       126
$\chi(\sigma)$       119
$\ddot{A}$       52
$\delta_{ij}$       5
$\epsilon(\sigma)$       113
$\eta(T)$       24
$\Gamma_{r,n}$       125
$\rho(A)$       82
$\rho(T)$       24
$\|u\|$       31
(u,v)      29
1-1 transformation      65
A*      52
Addition, vector      3
Additive identity      2
Additive inverse      2
adj A      136
Adjoint      52
Adjugate      136
Arithmetic-geometric mean inequality      170
Associativity      2
Associativity of matrix multiplication      50
Basis      5
Basis, o.n.      31
Basis, standard      5
Bessel's inequality      39
Bilinear function      58
Bilinearity, conjugate      30
Block multiplication of matrices      94
Brauer, A.      198
C(a)      79
Canonical form of a matrix      106
Cassini ovals      198
Cauchy number      112
Cauchy — Binet theorem      128
Cauchy — Schwarz inequality      40
Cauchy's inequalities      203
Cayley — Hamilton theorem      163
Characteristic equation      148
Characteristic matrix      147
Characteristic polynomial      147
Characteristic root      144
Characteristic vector      144
Coefficients      4 146
Column of a matrix      47
Column operations, elementary      91
Column rank of a matrix      79
Column space of a matrix      79
Commutative ring      2
Commutativity      2
Complementary sequence      126
Conformal partitioning      93
Conjugate bilinearity      30
Conjugate of a matrix      52
Conjugate symmetry      29
Conjugate transpose of a matrix      52
Coordinate vector      78
Courant — Fischer theorem      201
Cramer's rule      137
CYCLE      110
Cycles, disjoint      111
Degree of a polynomial      146
det (A)      120
Determinant      120
Determinant, expansion by column      135
Determinant, expansion by row      135
Determinant, Laplace expansion of      130 132
Diagonal corresponding to a permutation      119
Diagonal matrix      47
Diagonal of a matrix      119
Diagonal product      119
Diagonal, main      47
dim V      10
DIMENSION      10
Direct sum of matrices      95
Direct sum of subspaces      35
Disjoint cycles      111
Distributive law for transformations      18
Distributive laws of matrix multiplication      50
Distributivity      2
Eigenvalue      144
Eigenvector      144
Element of a matrix      47
Elementary column matrices      92
Elementary column operations      91
Elementary column operations, $III^{c(i)}$       91
Elementary column operations, $II^{(i),c(j)}$       91
Elementary column operations, $I^{(i),(j)}$       91
Elementary matrices      91
Elementary row operations      89
Elementary row operations, $III_{c(i)}$       89
Elementary row operations, $II_{(i)+c(j)}$       89
Elementary row operations, $I_{(i),(j)}$       89
Elementary symmetric function      149
Entry of a matrix      47
Equation, characteristic      148
Equivalence, unitary      158
Equivalent matrices      93
Equivalent systems      87
Euclidean space      31
Even permutations      112
Expansion by column      135
Expansion by row      135
Finite dimensional      5
Fixed vector      143
Gersgorin's disks      197
Gersgorin's theorem      197
Gram matrix      182
Gram — Schmidt process      32
Hadamard determinant theorem      199
Hermite normal form      99
Hermitian matrix      56
Hermitian transformation      56
Homogeneous linear equations      25 78
Homomorphism      16
Idempotent      165

Identity matrix      47
Identity transformation      18
Identity, additive      2
Identity, multiplicative      2
Independent indeterminates      146
Indeterminate      145
Inner product      29 30
Intersection of subspaces      36
Intersection of subspaces, $W_{1}\cap W_{2}$       36
Invariant subspace      64 99 143
Inverse of a matrix      70
Inverse of a transformation      64
K-cycle      110
ker T      18
Kernel of a transformation      18
Kronecker delta      5
L(U,V)      18
Laplace expansion theorem      130 132
latent root      144
Latent vector      144
Length of a vector      31
Length of orbit      111
linear combination      4
Linear dependence      4
Linear equations      24 78 137
Linear equations, homogeneous      25 78
Linear equations, nonhomogeneous      25
Linear extension of a transformation      21
Linear independence      5
Linear mapping      16
Linear transformation      16
Linear transformation, matrix representation of      46
Linearity of inner product      29
Lower triangular matrix      155
Main diagonal      47
Mapping, linear      16
Matrices, block multiplication of      94
Matrices, direct sum of      95
Matrices, elementary      91
Matrices, equivalent      93
Matrices, product of      49
Matrices, row equivalent      93
Matrices, sum of      49
Matrix      46
Matrix multiplication, associativity of      50
Matrix multiplication, distributive laws of      50
Matrix over Ry      46
Matrix polynomial      162
Matrix representation of a transformation      46
Matrix similarity      74
Matrix, canonical form of      106
Matrix, characteristic      147
Matrix, column of      47
Matrix, column rank of      79
Matrix, column space of      79
Matrix, conjugate of      52
Matrix, conjugate transpose of      52
Matrix, diagonal      47
Matrix, diagonal of      119
Matrix, element of      47
Matrix, entry of      47
Matrix, Gram      182
Matrix, Hermite normal form of      99
Matrix, hermitian      56
Matrix, identity      47
Matrix, inverse of      70
Matrix, lower triangular      155
Matrix, n-square      47
Matrix, nonsingular      70
Matrix, normal      56
Matrix, null space of      78
Matrix, orthogonal      56
Matrix, permutation      164
Matrix, powers of      50
Matrix, rank of      82
Matrix, row of      47
Matrix, row rank of      79
Matrix, row space of      79
Matrix, scalar product of      50
Matrix, singular      70
Matrix, skew-Hermitian      56
Matrix, skew-symmetric      56
Matrix, symmetric      56
Matrix, transpose of      51
Matrix, triangular      155
Matrix, unit      69
Matrix, unitary      56
Matrix, upper triangular      155
Matrix, zero      47
Maximal set      11
Monomial      145
Multiplication scalar      3
Multiplication, scalar      17
Multiplicative identity      2
Multiplicative inverse      2
n-square matrix      47
n-tuples      4
Nilpotent      165
Nonhomogeneous linear equations      25
Nonnegative hermitian matrix      182
Nonsingular matrix      70
Nonsingular transformation      65
Norm      31
Normal matrix      56
Normal transformation      56
Null space of a matrix      78
Nullity of a transformation      24
O.n.      31
O.n. basis      31
Odd permutations      112
One-one transformation      65
Onto transformation      65
Orbit      111
Orthogonal      31
Orthogonal complement      31
Orthogonal matrix      56
Orthogonal similarity      158
Orthogonal transformation      56
Orthonormal      31
Ostrowski, A.      198
Parseval's identity      40
per (A)      120
Permanent      120
Permanent, Laplace expansion of      142
Permutation      108
Permutation matrix      164
Permutation, even and odd      112
Permutation, signum of      113
Perpendicular      31
Polar factorization theorem      188
Polynomial      145
Polynomial, characteristic      147
Polynomial, matrix      162
Positive definite      29 182
Positive semidefinite      182
Powers of a matrix      50
Principal subdeterminant      126
Principal submatrix      126
Product of matrices      49
Product of permutations      108
Product of transformations      17
Product, inner      29
Projection theorem      36
Proper value      144
Ptoper vector      144
Quadratic function      58
r(A)      79
Range of a transformation      18
Rank of a matrix      82
Rank of a transformation      24

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