## Matrix Norm

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.
For an Matrix and an Unitary Matrix ,

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.

See also Compatible, Hilbert-Schmidt Norm, Maximum Absolute Column Sum Norm, Maximum Absolute Row Sum Norm, Natural Norm, Norm, Polynomial Norm, Spectral Norm, Spectral Radius, Vector 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.