
000 | 00000cam u2200205 a 4500 | |
001 | 000045838507 | |
005 | 20150715173101 | |
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 |
소장정보
No. | 소장처 | 청구기호 | 등록번호 | 도서상태 | 반납예정일 | 예약 | 서비스 |
---|---|---|---|---|---|---|---|
No. 1 | 소장처 과학도서관/Sci-Info(2층서고)/ | 청구기호 512.5 B215L | 등록번호 121233672 | 도서상태 대출가능 | 반납예정일 | 예약 | 서비스 |
컨텐츠정보
목차
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 matricesSystems of Linear Equations
Introduction
Gaussian elimination
Gauss-Jordan elimination
Elementary matrices
Homogeneous linear systems
The inverse of a matrixMore 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 formulaEuclidean 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 dimensionThe 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 formComplementary Subspaces
Sum of subspaces
The dimension of the sum of subspaces
Direct sums and complements
ProjectorsOrthogonality, 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 algebraMore on Orthogonality
Orthogonal matrices
The QR decomposition
Orthogonal projection and projector
Orthogonal projector: Alternative derivations
Sum of orthogonal projectors
Orthogonal triangularizationRevisiting 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 inverseDeterminants
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 expansionEigenvalues 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 decompositionSingular 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 formQuadratic 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 diagonalizationThe 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 productLinear 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 equationsAbstract 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 spacesReferences
Exercises appear at the end of each chapter.
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