Question
For A R n m , let A = i = 1 m i n ( n , m ) i where i are the
ForARnm , letA=i=1min(n,m)i where i are the singular values of A. Show thatA is a norm.
A norm verifies the following points:
(i) Homogeneity: v=||vf or all R and vV.
(ii) Triangular inequality: u + v u + v for all u, v V .
(iii) Positive definiteness: if v = 0 for some v V , then v = 0.
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Numerical Analysis
Authors: Richard L. Burden, J. Douglas Faires
9th edition
538733519, 978-1133169338, 1133169333, 978-0538733519
