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Matrices with Applications in Statistics

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ISBN-10: 0534401317

ISBN-13: 9780534401313

Edition: 2nd 2002 (Revised)

Authors: Franklin A. Graybill

List price: $199.95
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Part of the Duxbury Classic series, Franklin A. Graybill?s MATRICES WITH APPLICATIONS TO STATISTICS focuses primarily on matrices as they relate to areas of multivariate analysis and the linear model. This seminal work is a time tested, authoritative resource for both students and researchers.
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Book details

List price: $199.95
Edition: 2nd
Copyright year: 2002
Publisher: Brooks/Cole
Publication date: 12/28/2001
Binding: Paperback
Pages: 461
Size: 7.50" wide x 9.00" long x 1.00" tall
Weight: 1.782
Language: English

Prerequisite Matrix Theory
Introduction
Notation and definitions
Inverse
Transpose of a matrix
Determinants
Rank of matrices
Quadratic forms
Orthogonal matrices
Prerequisite Vector Theory
Introduction and definitions
Vector space
Vector subspaces
Linear dependence and independence
Basis of a vector space
Inner product and orthogonality of vectors
Linear Transformations and Characteristic ROOTS
Linear transformations
Characteristics roots and vectors
Similar matrices
Symmetric matrices
Geometric Interpretations
Introduction
Lines in En
Planes in En
Projections
Algebra of Vector Spaces
Introduction
Intersection and sum of vector spaces
Orthogonal complement of a vector subspace
Column and null spaces of a matrix
Statistical applications
Functions of matrices
Generalized Inverse; Conditional Inverse
Introduction
Definition and basic theorems of generalized inverse
Systems of linear equations
Generalized inverses for special matrices
Computing formulas for the g-inverse
Conditional inverse
Hermite form of matrices
Systems of Linear Equations
Introduction
Existence of solutions to Ax=g
the number of solutions of the system Ax=g
approximate solutions to inconsistent systems of linear equations
Statistical applications
Least squares
Statistical applications
Patterned Matrices And Other Special Matrices
Introduction
Partitioned matrices
The inverse of certain patterned matrices
Determinants of certain patterned matrices
Characteristic equations and roots of some patterned matrices
Triangular matrices
Correlation matrix
Direct product and sum of matrices
Additional theorems
Circulants
Dominant diagonal matrices
Vandermonde and Fourier matrices
Permutation matrices
Hadamard matrices
Band and Toeplitz matrices
Trace and Vector of Matrices
Trace
Vector of a matrix
Commutation matrices
Integration and Differentiation
Introduction
Transformation of random variables
Multivariate normal density
Moments of density functions and expected values of random matrices
Evaluation of a general multiple integral
Marginal density function
Examples
Derivatives
Expected values of quadratic forms
Expectation of the elements of a Wishart matrix
Inverse Positive Matrices and Matrices With Non-Positive Off-Diagonal Elements
Introduction and definitions
Matrices with positive principal minors
Matrices with non-positive off-diagonal elements
M-matrices (z-matrices with positive principle minors)
Z-matrices with non-negative principal minors
Non-Negative Matrices; Idempotent and Tripotent Matrices; Projections
Introduction
Non-negative matrices
Idempotent matrices
Tripotent matrices
Projections
Additional theorems
Reference and Additional Readings
Index