The Transformation given by the system of equations

is denoted by the Matrix Equation

In concise notation, this could be written

where and are Vectors and

For every linear transformation there exists one and only one corresponding matrix. Conversely, every matrix corresponds to a unique linear transformation. The matrix is an important concept in mathematics, and was first formulated by Sylvester and Cayley.

Two matrices may be added (Matrix Addition) or multiplied (Matrix Multiplication) together to yield a new
matrix. Other common operations on a single matrix are diagonalization, inversion (Matrix Inverse), and transposition
(Matrix Transpose). The Determinant
or
of a matrix *A* is a very important
quantity which appears in many diverse applications. Matrices provide a concise notation which is extremely useful in a wide
range of problems involving linear equations (e.g., Least Squares Fitting).

**References**

Arfken, G. ``Matrices.'' §4.2 in *Mathematical Methods for Physicists, 3rd ed.*
Orlando, FL: Academic Press, pp. 176-191, 1985.

© 1996-9

1999-05-26