Matrix Theory - Paperback

Matrix Theory: Essential Mathematical Foundation for Engineers and Scientists

Matrix Theory by Joel N. Franklin provides a rigorous yet accessible introduction to matrix mathematics, developed from the author's course at the California Institute of Technology. This comprehensive textbook addresses the fundamental role of matrices in representing linear transformations between finite sets of numbers—a critical concept in modern computational mathematics.

Comprehensive Coverage of Matrix Mathematics

The book begins with a concise presentation of determinant theory, progressing through classical linear algebra. Students explore triangularizations of Hermitian and non-Hermitian matrices, followed by a detailed proof of Jordan's matrix theory. Advanced topics include variational principles, perturbation theory, and matrix numerical analysis, concluding with an introduction to linear computations.

Applications Across Multiple Disciplines

Not only is matrix theory significant in a wide range of fields mathematical economics, quantum physics, geophysics, electrical network synthesis, crystallography, and structural engineering, among others-but with the vast proliferation of digital computers, knowledge of matrix theory is a must for every modern engineer, mathematician, and scientist. Matrices represent linear transformations from a finite set of numbers to another finite set of numbers.

Since many important problems are linear, and since digital computers with finite memory manipulate only finite sets of numbers, the solution of linear problems by digital computers usually involves matrices.

Designed for Multiple Learning Paths

This Dover mathematics textbook meets diverse educational needs. The mathematically rigorous approach serves students of pure and applied mathematics, while its applications-oriented content benefits engineering, science, and social science students. The book provides essential preparation for numerical analysis and computer science applications.

Minimal Prerequisites Required

The book assumes very little mathematical preparation, and except for the single section on the continuous dependence of eigenvalues on matrices, a knowledge of elementary algebra and calculus is sufficient. This accessibility makes it suitable for undergraduate and graduate students beginning their study of matrix theory.