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Linear Algebra and Matrix Analysis for Statistics (2014) by Sudipto Banerjee and Anindya Roy pdf [Dr Soc]

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  Linear Algebra and Matrix Analysis for
Statistics by Sudipto Banerjee and Anindya Roy
  English | 2014 | ISBN: 1420095382 | 580 pages | PDF | 3 MB
  
  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.
  
  
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