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Linear algebra and matrix analysis for statistics

Linear algebra and matrix analysis for statistics (Loan 9 times)

Material type
단행본
Personal Author
Banerjee, Sudipto. Roy, Anindya, 1970-.
Title Statement
Linear algebra and matrix analysis for statistics / Sudipto Banerjee, Professor of Biostatistics, School of Public Health, University of Minnesota, U.S.A., Anindya Roy, Professor of Statistics, Department of Mathematics and Statistics, University of Maryland, Baltimore County, U.S.A.
Publication, Distribution, etc
Boca Raton :   CRC Press, Taylor & Francis Group,   c2014.  
Physical Medium
xvii, 565 p. : ill. ; 25 cm.
Series Statement
Chapman & Hall/CRC texts in statistical science series
ISBN
9781420095388 (hardback) 1420095382 (hardback)
요약
"Linear algebra and the study of matrix algorithms have become fundamental to the development of statistical models. Using a vector-space approach, this book provides an understanding of the major concepts that underlie linear algebra and matrix analysis. Each chapter introduces a key topic, such as infinite-dimensional spaces, and provides illustrative examples. The authors examine recent developments in diverse fields such as spatial statistics, machine learning, data mining, and social network analysis. Complete in its coverage and accessible to students without prior knowledge of linear algebra, the text also includes results that are useful for traditional statistical applications."--
General Note
"A Chapman & Hall book."  
Bibliography, Etc. Note
Includes bibliographical references (p. 555-557) and index.
Subject Added Entry-Topical Term
Algebras, Linear. Matrices. Mathematical statistics.
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001 000045838507
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008 150715s2014 flua b 001 0 eng d
010 ▼a 2014004884
020 ▼a 9781420095388 (hardback)
020 ▼a 1420095382 (hardback)
035 ▼a (KERIS)REF000017728526
040 ▼a DLC ▼b eng ▼c DLC ▼e rda ▼d DLC ▼d 211009
050 0 0 ▼a QA184.2 ▼b .B36 2014
082 0 0 ▼a 512/.5 ▼2 23
084 ▼a 512.5 ▼2 DDCK
090 ▼a 512.5 ▼b B215L
100 1 ▼a Banerjee, Sudipto.
245 1 0 ▼a Linear algebra and matrix analysis for statistics / ▼c Sudipto Banerjee, Professor of Biostatistics, School of Public Health, University of Minnesota, U.S.A., Anindya Roy, Professor of Statistics, Department of Mathematics and Statistics, University of Maryland, Baltimore County, U.S.A.
260 ▼a Boca Raton : ▼b CRC Press, Taylor & Francis Group, ▼c c2014.
300 ▼a xvii, 565 p. : ▼b ill. ; ▼c 25 cm.
490 1 ▼a Chapman & Hall/CRC texts in statistical science series
500 ▼a "A Chapman & Hall book."
504 ▼a Includes bibliographical references (p. 555-557) and index.
520 ▼a "Linear algebra and the study of matrix algorithms have become fundamental to the development of statistical models. Using a vector-space approach, this book provides an understanding of the major concepts that underlie linear algebra and matrix analysis. Each chapter introduces a key topic, such as infinite-dimensional spaces, and provides illustrative examples. The authors examine recent developments in diverse fields such as spatial statistics, machine learning, data mining, and social network analysis. Complete in its coverage and accessible to students without prior knowledge of linear algebra, the text also includes results that are useful for traditional statistical applications."-- ▼c Provided by publisher.
650 0 ▼a Algebras, Linear.
650 0 ▼a Matrices.
650 0 ▼a Mathematical statistics.
700 1 ▼a Roy, Anindya, ▼d 1970-.
830 0 ▼a Chapman & Hall/CRC texts in statistical science series.
945 ▼a KLPA

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 512.5 B215L Accession No. 121233672 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents

Matrices, Vectors, and Their Operations
Basic definitions and notations
Matrix addition and scalar-matrix multiplication
Matrix multiplication
Partitioned matrices
The "trace" of a square matrix
Some special matrices

Systems of Linear Equations
Introduction
Gaussian elimination
Gauss-Jordan elimination
Elementary matrices
Homogeneous linear systems
The inverse of a matrix

More on Linear Equations
The LU decomposition
Crout’s Algorithm
LU decomposition with row interchanges
The LDU and Cholesky factorizations
Inverse of partitioned matrices
The LDU decomposition for partitioned matrices
The Sherman-Woodbury-Morrison formula

Euclidean Spaces
Introduction
Vector addition and scalar multiplication
Linear spaces and subspaces
Intersection and sum of subspaces
Linear combinations and spans
Four fundamental subspaces
Linear independence
Basis and dimension

The Rank of a Matrix
Rank and nullity of a matrix
Bases for the four fundamental subspaces
Rank and inverse
Rank factorization
The rank-normal form
Rank of a partitioned matrix
Bases for the fundamental subspaces using the rank normal form

Complementary Subspaces
Sum of subspaces
The dimension of the sum of subspaces
Direct sums and complements
Projectors

Orthogonality, Orthogonal Subspaces, and Projections
Inner product, norms, and orthogonality
Row rank = column rank: A proof using orthogonality
Orthogonal projections
Gram-Schmidt orthogonalization
Orthocomplementary subspaces
The fundamental theorem of linear algebra

More on Orthogonality
Orthogonal matrices
The QR decomposition
Orthogonal projection and projector
Orthogonal projector: Alternative derivations
Sum of orthogonal projectors
Orthogonal triangularization

Revisiting Linear Equations
Introduction
Null spaces and the general solution of linear systems
Rank and linear systems
Generalized inverse of a matrix
Generalized inverses and linear systems
The Moore-Penrose inverse

Determinants
Definitions
Some basic properties of determinants
Determinant of products
Computing determinants
The determinant of the transpose of a matrix ? revisited
Determinants of partitioned matrices
Cofactors and expansion theorems
The minor and the rank of a matrix
The Cauchy-Binet formula
The Laplace expansion

Eigenvalues and Eigenvectors
Characteristic polynomial and its roots
Spectral decomposition of real symmetric matrices
Spectral decomposition of Hermitian and normal matrices
Further results on eigenvalues
Singular value decomposition

Singular Value and Jordan Decompositions
Singular value decomposition (SVD)
The SVD and the four fundamental subspaces
SVD and linear systems
SVD, data compression and principal components
Computing the SVD
The Jordan canonical form
Implications of the Jordan canonical form

Quadratic Forms
Introduction
Quadratic forms
Matrices in quadratic forms
Positive and nonnegative definite matrices
Congruence and Sylvester’s law of inertia
Nonnegative definite matrices and minors
Extrema of quadratic forms
Simultaneous diagonalization

The Kronecker Product and Related Operations
Bilinear interpolation and the Kronecker product
Basic properties of Kronecker products
Inverses, rank and nonsingularity of Kronecker products
Matrix factorizations for Kronecker products
Eigenvalues and determinant
The vec and commutator operators
Linear systems involving Kronecker products
Sylvester’s equation and the Kronecker sum
The Hadamard product

Linear Iterative Systems, Norms, and Convergence
Linear iterative systems and convergence of matrix powers
Vector norms
Spectral radius and matrix convergence
Matrix norms and the Gerschgorin circles
SVD ? revisited
Web page ranking and Markov chains
Iterative algorithms for solving linear equations

Abstract Linear Algebra
General vector spaces
General inner products
Linear transformations, adjoint and rank
The four fundamental subspaces - revisited
Inverses of linear transformations
Linear transformations and matrices
Change of bases, equivalence and similar matrices
Hilbert spaces

References

Exercises appear at the end of each chapter.


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