Matrix Algebra and Its Applications to Statistics and EconometricsWorld Scientific, 1998 - 535 sidor Written by two top statisticians with experience in teaching matrix methods for applications in statistics, econometrics and related areas, this book provides a comprehensive treatment of the latest techniques in matrix algebra. A well-balanced approach to discussing the mathematical theory and applications to problems in other areas is an attractive feature of the book. It can be used as a textbook in courses on matrix algebra for statisticians, econometricians and mathematicians as well. Some of the new developments of linear models are given in some detail using results of matrix algebra. |
Innehåll
VECTOR SPACES | 1 |
UNITARY AND EUCLIDEAN SPACES | 51 |
LINEAR TRANSFORMATIONS | 107 |
CHARACTERISTICS OF MATRICES | 127 |
FACTORIZATION OF MATRICES | 157 |
OPERATIONS ON MATRICES | 193 |
PROJECTORS AND IDEMPOTENT | 239 |
GENERALIZED INVERSES | 263 |
Theorem | 340 |
MATRIX APPROXIMATIONS | 361 |
OPTIMIZATION PROBLEMS | 403 |
QUADRATIC SUBSPACES | 433 |
INEQUALITIES WITH APPLICATIONS | 449 |
NONNEGATIVE MATRICES | 467 |
MISCELLANEOUS COMPLEMENTS | 493 |
| 519 | |
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Matrix Algebra And Its Applications To Statistics And Econometrics Calyampudi Radhakrishna Rao,Mareppalli Bhaskara Rao Begränsad förhandsgranskning - 1998 |
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A₁ B₁ basis column vector Complements completes the proof complex numbers compute conjugate bilinear functional Consequently COROLLARY decomposition defined definite matrix denoted diagonal entries eigenvalues eigenvectors elements exists field F g-inverse given Hermitian conjugate Hermitian matrix idempotent inequality inner product space integer inverse latin squares Let A1 linear combination linear equations linear functional linearly independent m x m m x n matrix norm matrix of order Mm,n multiplication non-negative definite non-singular Note obtained operation order m x order mxn order n x n orthonormal P₁ permutation permutation matrix positive definite problem projector properties ps(A quadratic subspace rank real numbers respectively S₁ scalars semi-inner product Show singular value decomposition singular values solution Sp(A spectral square matrix submatrix subspace Suppose symmetric matrix Theorem unbiased estimator unique unitary matrix V₁ vector space y₁ zero ах
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