Linear Algebra Solved Problems

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This book is a continuation of the book n-linear algebra of type I.

Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure which is introduced in this book.n-Linear Algebra of type I introduced in this book finds applications in Markov chains and Leontief economic models.

All examples are solved, and the solutions consist of step-by-step instructions, and are designed to assist students in methodically solving problems.

The primary focus of this book is to provide a readable account in modern notation of Grassmann's major algebraic contributions to mathematics and science.

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.

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.

As my main object has been to produce a textbook suitable for beginners, many important theorems have been omitted.

From the table of contents: Linear second order ODEs; Homogeneous linear ODEs; Non-homogeneous linear ODEs; Laplace transforms; Linear algebraic equations; Matrix Equations; Linear algebraic eigenvalue problems; Systems of differential equations.

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