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.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!