Let be a Vector Norm of such that

Then is a Matrix Norm which is said to be the natural norm Induced (or Subordinate) to the Vector Norm . For any natural norm,

where is the Identity Matrix. The natural matrix norms induced by the L1-Norm, L2-Norm, and L(infinity)-Norm are called the Maximum Absolute Column Sum Norm, Spectral Norm, and Maximum Absolute Row Sum Norm, respectively.

**References**

Gradshteyn, I. S. and Ryzhik, I. M. *Tables of Integrals, Series, and Products, 5th ed.* San Diego, CA:
Academic Press, p. 1115, 1979.

© 1996-9

1999-05-25