Matrix Algebra and Its Applications to Statistics and Econometrics
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.
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UNITARY AND EUCLIDEAN SPACES
CHARACTERISTICS OF MATRICES
FACTORIZATION OF MATRICES
OPERATIONS ON MATRICES
PROJECTORS AND IDEMPOTENT
INEQUALITIES FOR EIGENVALUES
INEQUALITIES WITH APPLICATIONS
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A G Mm,n basis Cauchy-Schwartz inequality column vector Complements completes the proof complex numbers compute conjugate bilinear functional Consequently Corollary defined definite matrix denoted df/dX diagonal entries eigenvalues eigenvectors elements exists field F given Hermitian conjugate Hermitian matrix i-th idempotent identity inequality inner product space integer inverse latin squares Let A G Mn linear combination linear equations linear functional linear transformation linearly independent m x n matrix norm matrix of order multiplication n x n non-negative definite non-singular non-singular matrix non-zero vector Note obtained operation order m x m order mxn orthogonal projection orthonormal permutation permutation matrix positive definite projector properties ps(A quadratic subspace rank real numbers respectively scalars semi-inner product Show singular value decomposition singular values solution Sp(A square matrix submatrix subspace Suppose symmetric matrix Theorem unbiased estimator unique unitary matrix vector of order vector space zero