Given a Square Matrix with Complex (or Real) entries, a Matrix Norm is a Nonnegative number associated with having the properties

- 1. when and Iff ,
- 2. for any Scalar ,
- 3. ,
- 4.

Let , ..., be the Eigenvalues of , then

The Maximum Absolute Column Sum Norm
, Spectral Norm
, and
Maximum Absolute Row Sum Norm
satisfy

For a Square Matrix, the Spectral Norm, which is the Square Root of the maximum Eigenvalue of (where is the Adjoint Matrix), is often referred to as ``the'' matrix norm.

**References**

Gradshteyn, I. S. and Ryzhik, I. M. *Tables of Integrals, Series, and Products, 5th ed.* San Diego, CA:
Academic Press, pp. 1114-1125, 1979.

© 1996-9

1999-05-26