Matrix Norm
Given a Square Matrix 
with Complex (or Real) entries, aMatrix Norm 
is a Nonnegative number associated with having the properties
- 1.
when 
and 
Iff 
, - 2.
for any Scalar 
, - 3.
, - 4.
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'' matrixnorm.See also Compatible, Hilbert-Schmidt Norm, Maximum Absolute Column Sum Norm, Maximum Absolute RowSum 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.
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