Linear Algebra Solved Problems

Linear Algebra Solved Problems-62
From the table of contents: K-modules and linear transformations; Linear independence, spanning, bases, and dimension; Coordinates, column vectors, and matrices; Eigenstuff; Multilinear algebra and tensors; Inner-product spaces; Applications.In the present treatise I have attempted to give an exposition of the Theory of Determinants and their more important applications.The treatise uses Grassmann's alternate units, by means of which the study of determinants is much simplified.

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Special Set Linear Algebras introduced by the authors in this free book is an extension of Set Linear Algebras, which are the most generalized form of linear algebras.

Topics: Matrices, Moments and Quadrature; Structured Approaches to General Inverse Eigenvalue Problems; Eigenvalue Problems; Nonnegative Inverse Elementary Divisors Problem; Some Recent Advances in Nonlinear Inverse Scattering in 2D; and more.

This book is a text for a graduate course that focuses on applications of linear algebra and on the algorithms used to solve the problems that arise in those applications.

Tthe particular nature of the applications will prompt us to seek algorithms.

Contents: Vectors and Vector Spaces; Matrices and Linear Algebra; Eigenvalues and Eigenvectors; Unitary Matrices; Hermitian Theory; Normal Matrices; Factorization Theorems; Jordan Normal Form; Hermitian and Symmetric Matrices; Nonnegative Matrices.

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