Description
Linear Algebra and Matrix Analysis for Statistics
Chapman & Hall/CRC Texts in Statistical Science Series
Authors: Banerjee Sudipto, Roy Anindya
Language: EnglishSubjects for Linear Algebra and Matrix Analysis for Statistics:
Keywords
Linearly Independent; Elementary Row Operations; Fundamental Theorem Of Linear Algebra; Nonsingular Matrix; Computational Techniques For Orthogonal Reduction; Row Echelon Form; Undergraduate Course In Linear Algebra; Null Space; Hilbert Spaces; Full Column Rank; Algorithms For Eigenvalues And Eigenvectors; Rank Nullity Theorem; Kronecker And Hadamard Products; Fundamental Subspaces; Gaussian Elimination; QR Decomposition; Orthonormal Basis; Permutation Matrix; LU Decomposition; Nonnegative Definite; Echelon Matrix; Orthogonal Projection; Full Row Rank; Vector Space; Spectral Decomposition; Gauss Jordan Elimination; Row Interchanges; RREF; System Ax; LU Factor; Real Symmetric Matrix
416 p. · 15.6x23.4 cm · Hardback
Description
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Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra.
The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction.
The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.
Matrices, Vectors, and Their Operations. Systems of Linear Equations. More on Linear Equations. Euclidean Spaces. The Rank of a Matrix. Complementary Subspaces. Orthogonality, Orthogonal Subspaces, and Projections. More on Orthogonality. Revisiting Linear Equations. Determinants. Eigenvalues and Eigenvectors. Quadratic Forms. The Kronecker Product and Related Operations. Linear Iterative Systems, Norms, and Convergence. Abstract Linear Algebra. References.
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