Linear Algebra, Matrix Theory and Applications

Description

Matrices are more than arrays of numbers: they offer a common language for solving systems, describing transformations, and approaching problems across mathematics and its applications. Edited by Stefano Spezia, Linear Algebra, Matrix Theory and Applications gathers material on the subject’s essential concepts alongside more specialized matrix methods.

From elimination to vector spaces

The opening sections cover matrices and Gaussian elimination, then turn to vector spaces, least-squares regression, and the Gram–Schmidt process. Together, these topics connect practical computation with the structure that makes linear algebra useful.

Key ideas in matrix theory

Further sections address determinants; eigenvalues and eigenvectors; positive definite matrices; and singular value decomposition. The range gives readers a path through several central tools for understanding and working with matrices.

Methods and applications

The book continues with computations involving matrices and linear programming, followed by the Jordan form and the principal matrix pth root. It also discusses topics such as Gaussian-elimination-based correlation analysis, fast matrix multiplication, and diagonalization methods for spin chains.

A broad reference for mathematical study

Rather than focusing on a single technique, this edited volume spans foundational concepts and more focused applications. It may suit students and readers of mathematics who want to revisit core linear algebra topics or explore a wider selection of matrix-related methods.

For a study session on fundamentals or a closer look at matrix theory’s varied applications, this volume offers a substantial collection of material in one place.