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Fuzhen Zhang — Matrix theory: basic results and techniques
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Название: Matrix theory: basic results and techniquesАвтор: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1 editionГод издания: 1999Количество страниц: 290Добавлена в каталог: 31.10.2010Операции: Положить на полку |
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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, 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 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 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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