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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: 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 Предметный указатель (matrix exponential)      72 100 (matrix exponential) for a positive definite matrix      135 , norm      110 norm      110 , norm      110 norm      110 , 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
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