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Bronson R. — Schaum's Outline of Matrix Operations
Bronson R. — Schaum's Outline of Matrix Operations

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Название: Schaum's Outline of Matrix Operations

Автор: Bronson R.

Аннотация:

If you want top grades and thorough understanding of matrix operations, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you 363 accompanying related problems with fully worked solutions. You also get plenty of practice problems to do on your own, working at your own speed. (Answers at the back show you how you're doing.) Famous for their clarity, wealth of illustrations and examples, and lack of dreary minutiae, Schaum's Outlines have sold more than 30 million copies worldwide—and this guide will show you why!


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 230

Добавлена в каталог: 09.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$e^A$ (matrix exponential)      72 100
$e^A$ (matrix exponential) for a positive definite matrix      135
$l_1$, norm      110
$L_2$ norm      110
$L_p$, norm      110
$l_{\infty}$ norm      110
$L_{\infty}$, norm      110
Addition of matrices      2
Adjoint      119
Angle between vectors      143
Augmented matrix      11
AX + XB = C      73
AX = B      see “Simultaneous linear equations”
AXB = C      166
Band matrix      160
Bessel function      80
Block matrix      43
Canonical basis      82
Canonical basis for a normal matrix      119
Cayley — Hamilton theorem      61
Chain      82
Characteristic equation      60
Characteristic equation of similar matrices      91
Characteristic polynomial      60
Characteristic value      see “Eigenvalue”
Characteristic vector      see “Eigenvector”
Cholesky decomposition      129
Circulant matrix      160
Coefficient matrix      11
Cofactor      42 50
Cofactor matrix      44
Column rank      53
Column vector      1
Companion matrix      70
Compatible norms      111 116
Complete pivoting      19
Complex conjugate      103
Complex conjugate transpose matrix      119
Complex matrix      1 103
Complex quadratic form      144 (see also “Quadratic form”)
Component      52
Condition number      118
Congruent matrices      144 151
Conjunctive matrices      145
Consistency condition for norms      110
Consistent simultaneous equations      11
Constant matrix      1
Convex combination      59
Crout’s reduction      25
Crout’s reduction for a tridiagonal matrix      161
Derivative of a matrix      72
Determinant      42
Determinant and eigenvalues      60
Determinant for a unitary matrix      136
Determinant of a positive definite matrix      132
Determinant of an LU decomposition      51
Diagonal      24 127
Diagonal matrix      24 127 137
Diagonal quadratic form      144
Differential equations      72
DIMENSION      52
Direct product      165
Distance between vectors      110
Distribution vector      153
Dominant eigenvalue      111 152 169
Dot product      1
Doubly stochastic matrix      153
Eigenvalue      60
Eigenvalue rank number      82
Eigenvalue, bounds on      112
Eigenvalue, by numerical methods      169—170 181
Eigenvalue, by QR algorithm      181
Eigenvalue, dominant      111 152 169
Eigenvalue, for a unitary matrix      136
Eigenvalue, of a circulant matrix      160
Eigenvalue, of a Hermitian matrix      119
Eigenvalue, of a nonnegative matrix      152
Eigenvalue, of a positive definite matrix      128
Eigenvalue, of a positive matrix      152
Eigenvalue, of a singular matrix      60
Eigenvalue, of a transpose      60
Eigenvalue, of a triangular matrix      60
Eigenvalue, of an elementary reflector      143
Eigenvalue, of an inverse      60
Eigenvalue, of f(A)      93
Eigenvalue, of similar matrices      91
Eigenvector      60
Eigenvector, by numerical methods      169 170
Eigenvector, generalized      82
Eigenvector, maximal linearly independent set of      61
Eigenvector, of a circulant matrix      160
Eigenvector, of a Hermitian matrix      119
Eigenvector, of a nonnegative matrix      152 153
Eigenvector, of a normal matrix      119
Eigenvector, of a real symmetric matrix      119
Elementary column operations      3
Elementary matrix      24
Elementary matrix, determinant of      43
Elementary matrix, inverse of      34
Elementary reflector      137
Elementary row operations      3
Equality of matrices      1
Ergodic matrix      153
Euclidean inner product      103 120
Euclidean matrix norm      111
Euclidean vector norm      110 116 194
Expansion by cofactors      42
Exponential of a matrix      71
Finite Markov chain      153
Frobenius norm      111 116
Function of a matrix      71 92
Function of a matrix, eigenvalues of      93
Function of a matrix, Hermitian      127
Gauss — Jordan elimination      21
Gaussian elimination      12
Generalized eigenvector      82
Generalized inverse      192
Gerschgorin’s theorem      170
Given’s method      167
Gram — Schmidt orthogonalization process      104 121
Gram — Schmidt orthogonalization process, modified      181
Hermitian congruent matrices      145
Hermitian matrix      119
Hermitian matrix, eigenvalues of      119
Hermitian matrix, for a quadratic form      144
Hermitian matrix, functions of      127
Hermitian matrix, generalized inverse of      192
Hermitian matrix, positive definite      128
Hermitian matrix, Rayleigh’s quotient      146
Hermitian transpose matrix      119
Hermitian transpose matrix, for a unitary matrix      136
Hessenberg form      161 182
Homogeneous linear equations      12 23 55 59
Householder transformation      137
Idempotent matrix      33 202
Identity matrix      24 118
Inconsistent simultaneous equations      11
INDEX      145
Index, of a nilpotent matrix      32
Induced norm      111
Inertia matrix      145
Infinite series of matrices      71
Inner product      103 136 144
Integral of a matrix      72
Inverse      34 44
Inverse power method      170
Inverse power method, modified      180
Inverse, and congruence      151
Inverse, by row reduction      34
Inverse, determinant of      43
Inverse, eigenvalue of      60
Inverse, of a circulant matrix      160
Inverse, of a unitary matrix      136
Inverse, of an elementary matrix      34
Inverse, of an orthogonal matrix      136
Invertible      34
Irreducible matrix      152
Jordan block      91
Jordan canonical form      91
Kronecker product      165
Least squares      194 201
Left eigenvector      67 154
Length, of a chain      82
Length, of a vector      110 143
linear combination      52
Linear combination, of eigenvectors      66
Linear dependence      52 53
Linear equations      see “Simultaneous linear equations”
Linear independence      52 53
Linear independence of a chain      85
Linear independence of eigenvectors      61
Lower triangular matrix      24
Lower triangular matrix, determinant of      42
Lower triangular matrix, eigenvalues of      60
Lower triangular matrix, inverse of      32
LU decomposition      24 40 51
LU decomposition, Cholesky decomposition      129
LU decomposition, Crout’s reduction      25 161
Magnitude of a vector      110
Main diagonal      24
Markov chain      153
Matrix      1
Matrix equation AX + XB = C      73
Matrix equation AX + XB = C, AX = B      see “Simultaneous linear equations”
Matrix equation AX + XB = C, AXB = C      166
Matrix norm      110
Maximal set of linearly independent vectors      57
Maximal set of linearly independent vectors, eigenvectors      61
Minimum polynomial      83
Minor      42
Minor, principal      128
Modal matrix      91
Modified Gram — Schmidt process      174
Moore — Penrose inverse      192
Multiplication of matrices      2 6
Negative definite matrix      128
Negative semidefinite matrix      128
Nilpotent      32
Nonhomogeneous linear equations      12 (see also “Simultaneous linear equations”)
Nonnegative matrix      152
Nonsingular matrix      34
Nontrivial solutions      12
Norm      110
Normal equations      201
Normal matrix      119 136
Normal matrix, similar to a diagonal matrix      137
Normalized vector      110
Null space      59
Numerical methods for eigenvalues      169 170 181
Order      1
Orthogonal matrix      136 137
Orthogonal vectors      103
Orthonormal vectors      110 119 136
Partial pivoting      13 (see also “Pivoting strategies”)
Partitioned matrix      5
Partitioned matrix, determinant of      43
Permutation matrix      152
Perpendicular      see “Orthogonal vectors”
Perron — Frobenius theorem      152
Perron’s theorem      152
Pivot      3
Pivotal condensation      43
Pivoting strategies      12 18 19 25 35
Polar decomposition      202
Positive definite matrix      128
Positive matrix      152
Positive semidefinite matrix      128
Power method      169
Power method, modified      174
Powers of a matrix      26
Primitive matrix      153
Principal diagonal      24
Principal minor      128
Pseudoinverse      192
QR algorithm      181
QR decomposition      181 201
Quadratic form      144
Rank number of an eigenvalue      82
Rank, of a generalized eigenvector      82
Rank, of a matrix      3 12 43 53 144 192
Rayleigh’s principle      146
Rayleigh’s quotient      146 174 180
Real matrix      1
Real symmetric matrix      119 161 174
Real symmetric matrix for a quadratic form      144
Reducible matrix      152
Regular matrix      153
Right eigenvector      60 (see also “Eigenvector”)
Rotation matrix      143 167
Row rank      3 53
Row vector      1
Row-echelon form      2
Row-echelon form, reduction to      3
scalar      1
Scalar multiplication      2
Scaled pivoting      18
Schur decomposition      136
Schwarz inequality      103
Self-adjoint matrix      120
Sequences of matrices      71
Series of matrices      71
Shifted inverse power method      170
Shifted inverse power method, modified      180
Shifted QR algorithm      182
Signature      145
Similar matrices      91 123
Similarity transformation      137
Similarity transformation, QR algorithm      188
Simultaneous linear equations      11 25 35
Simultaneous linear equations, homogeneous      12 55 59
Simultaneous linear equations, matrix form      11 (see also “Solutions of simultaneous linear equations”)
Singular matrix      34
Singular matrix, eigenvalues of      60
Singular value      193
Singular value decomposition      193
Skew-Hermitian matrix      127
Skew-symmetric matrix      127
Solutions of simultaneous linear equations      11
Solutions of simultaneous linear equations, by Gauss — Jordan elimination      21
Solutions of simultaneous linear equations, by Gaussian elimination      12
Solutions of simultaneous linear equations, by inversion      35
Solutions of simultaneous linear equations, by LU decomposition      25
Solutions of simultaneous linear equations, least squares      194
Solutions of simultaneous linear equations, theory of      12 23 55
Solutions of simultaneous linear equations, trivial      12
Spectral norm      111 141
Spectral radius      111 118
Spectral radius, for nonnegative matrices      152
Square matrix      24
Square root of a matrix      128
Stochastic matrix      153 158
Subdiagonal      24
Subtraction of matrices      2
Superdiagonal      24
Sylvester’s law of inertia      145
Symmetric matrix      see “Real symmetric matrix”
Toeplitz matrix      160 161
Trace      60 70 91 172
TRANSPOSE      1
Transpose, determinant of      43
1 2
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