Let x be a m - vector, A be an m x n matrix, show that (1) infinity norm x <= 2nd norm x <= square root (m) * infinity norm x (2) [1/square root(n)] * infinity norm A <=2nd norm A <= square root (m) * infinity norm A
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Hello, Originally Posted by tinng Let x be a m - vector, A be an m x n matrix, show that (1) infinity norm x <= 2nd norm x <= square root (m) * infinity norm x (2) [1/square root(n)] * infinity norm A <=2nd norm A <= square root (m) * infinity norm A Get back to the definitions of the norms : You'll have to use two inequalities : - Triangle inequality : - Cauchy-Schwarz inequality :
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