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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