This book is intended as an undergraduate text introducing matrix methods as they relate to engineering problems. It begins with the fundamentals of mathematics of matrices and determinants. Matrix inversion is discussed, with an introduction of the well known reduction methods. Equation sets are viewed as vector transformations, and the conditions of their solvability are explored. Orthogonal matrices are introduced with examples showing application to many problems requiring three dimensional thinking. The angular velocity matrix is shown to emerge from the differentiation of the 3-D orthogonal matrix, leading to the discussion of particle and rigid body dynamics.

The book continues with the eigenvalue problem and its application to multi-variable vibrations. Because the eigenvalue problem requires some operations with polynomials, a separate discussion of these is given in an appendix. The example of the vibrating string is given with a comparison of the matrix analysis to the continuous solution.

### Table of Contents

Matrix Fundamentals

Determinants

Matrix Inversion

Linear Simultaneous Equation Sets

Orthogonal Transforms

Matrix Eigenvalue Analysis

Matrix Analysis of Vibrating Systems

### About the Author(s)

**Marvin Tobias**, General Electric

A native Utahn (Salt Lake), Marvin J. Tobias graduated in Mechanical Engineering (ME) from the University of Utah. He joined the General Electric Company and began a series of rotating assignments through various Departments in the East, initially in the General Engineering Laboratory, then in the Jet Engine Department. In the fall, Marv successfully applied for a three year intensive training program; the Advanced Engineering Program. During the latter years of the program his assignments were in radar signal and data processing. Assignments in both ME and EE proved the need for further education and training in mathematics, so the middle year (B courseâ€”applied mathematics) was particularly interesting. Over the years, Marv became a lecturer for the B course, developing many notes on matrix algebra and calculus. As the PC became more powerful, with sophisticated word processing and graphics software, those notes became the content of this book.