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Fuzhen Zhang — Matrix theory: basic results and techniques
Fuzhen Zhang — Matrix theory: basic results and techniques

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Название: Matrix theory: basic results and techniques

Автор: Fuzhen Zhang

Аннотация:

The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains eight chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. For many theorems several different proofs are given. The book can be used as a text or a supplement for a linear algebra and matrix theory class or seminar for senior or graduate students. The only prerequisites are a decent background in elementary linear algebra and calculus. The book can also serve as a reference for instructors and researchers in the fields of algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other fields. (Solutions manual available for qualified instructors upon request.)


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1999

Количество страниц: 290

Добавлена в каталог: 31.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Addition      1
Adjoint      10
angle      25
Basis      2
Birkhoff, G.      127
Cauchy interlacing theorem      221
Cauchy sequence      142
Cauchy — Schwarz inequality      22 203 255
Cayley — Hamilton      70
Characteristic polynomial      18 70
Cofactor      10
Column space      49
Compact set      89 138
Complete space      142
conjugate      7
Continuity argument      36 56
Contraction      142
Convergence      142
Convex combination      127
Convex hull      92
Coordinate      3
Courant — Fischer      220
Decomposition, Jordan      74 78
Decomposition, polar      67
Decomposition, Schur      64
Decomposition, singular value      66
Decomposition, spectral      65
Decomposition, triangular      65
Determinant      9
Differential operator      14
DIMENSION      2
Dimension identity      4
Direct product      190
Direct sum      5 9
Eigenspace      19
Eigenvalue      16 18 51 219 227
Eigenvector      16
Elementary divisor      75
Elementary operation      8 30 74
Elementary symmetric function      113
Fan, K.      231 264
Field of values      88
Fischer Inequality      175
Fixed point      143
Frobenius — Koenig      126
Hadamard inequality      176
Hadamard product      190
Hoffman, A.      264
Hua inequality      187
Image      14
Inertia      212
Inner product      22
Inner product space      22
Interlacing theorem      222
Interpolation      60
Invariant factor      75
Invariant suhspace      19
Inverse      10 20 43
Involution      93
Isomorphism      21
Jordan block      74
Jordan canonical form      74
Jordan form      74
Kantorovich Inequality      204
Kernel      14
Kronecker product      190
Laplace expansion      9
Length      23
Linear dependence      2
Linear independence      2
Linear transformation      14
Loewner partial ordering      166
LU factorization      68
Majorization      229 262
Matrix      6 15
Matrix addition      6
Matrix product      6
Matrix, $\lambda$-      74
Matrix, (0, 1)-      251
Matrix, backward identity      13 81
Matrix, block      7
Matrix, Cauchy      105 197
Matrix, circulant      106
Matrix, complex orthogonal      131
Matrix, diagonal      7
Matrix, doubly stochastic      126
Matrix, elementary      8
Matrix, elementary $\lambda$-      75
Matrix, Fourier      108
Matrix, generalized elementary      30
Matrix, Hadamard      118
Matrix, hermitian      7 65 208
Matrix, idempotent      93
Matrix, identity      7
Matrix, invertible      10
Matrix, invertible $\lambda$-      75
Matrix, involutary      93
Matrix, irreducible      123
Matrix, nilpotent      93
Matrix, nonnegative definite      160
Matrix, nonsingular      10
Matrix, normal      7 65 240
Matrix, orthogonal      7
Matrix, partitioned      7
Matrix, permutation      123
Matrix, positive definite      159
Matrix, positive semidefinite      65 159
Matrix, primary permutation      106 124
Matrix, projection      93
Matrix, Real orthogonal      131
Matrix, reducible      123
Matrix, scalar      7
Matrix, skew-Hermitian      211
Matrix, skew-symmetric      57
Matrix, symmetric      7
Matrix, Topelitz      110
Matrix, tridiagonal      101
Matrix, unitary      7 131
Matrix, upper-triangular      7
Matrix, Vandermonde      11 110 111
Matrix, zero      7
Metric      143
Metric space      142
Minimal polynomial      71
Minor      20
Multiplicity      51
Norm      23
Null space      14
Numerical radius      89
Numerical range      88
Oppenheim, A.      200
Orthogonal projection      95
Orthogonal set      23
Orthogonal vector      23
Orthonormal set      23
Permutation      130
Permutation similarity      123
Poincare interlacing theorem      221
Primary permutation matrix      107 124
Primitive root      106
Principal submatrix      20
Projection      93 95 100
QR factorization      68
Rank      9 46
Rayleigh — Ritz      220
Real orthogonal projection      140
Reflection      137
Rotation      137
Row space      49
Scalar multiplication      1 6
Schur complement      175 184
Schur inequality      260
Schur product      190
Schur, I.      192 230
Similarity      15
Singular value      55 66 90 144 228
Solution space      9
span      2
Spectra) radius      90
Spectral norm      90
Square root      66 144 162
Standard basis      3
Standard form      75
Strict contraction      142
Sturm interlacing theorem      221
SubMatrix      7
subspace      3
Sum of subspaces      3
Sylvester, J.      46
Tensor product      190
Thompson, R.C.      237
Toeplitz — Hausdorff      88
Trace      18
TRANSPOSE      7
Triangle inequality      23
Triangularization      65
Unit vector      23
Unitary similarity      64
Vector      1
Vector space      1
Weak majorization      229 262
Wielant inequality      2 07
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