Matrix Algebra Introduction

Matrix Algebra: Introduction Matrices and Determinants were discovered and developed in the eighteenth and nineteenth centuries. Initially, their development dealt with transformation of geometric objects and solution of systems of linear equations. Historically, the early emphasis was on the determinant, not the matrix. In modern treatments of linear algebra, matrices are considered first. We will not speculate much on this issue. Matrices provide a theoretically and practically useful way of approaching many types of problems including: •

Solution of Systems of Linear Equations,

•

Equilibrium of Rigid Bodies (in physics),

•

Graph Theory,

•

Theory of Games,

•

Leontief Economics Model,

•

Forest Management,

•

Computer Graphics, and Computed Tomography,

•

Genetics,

•

Cryptography,

•

Electrical Networks,

•

Fractals.