Proof in Linear Algebra
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6. Suppose
A = [a,b: b,a]
where a and b area real numbers. Show that the subordinate matrix norms satsify ||A||1 = ||A||2 = ||A||_infinity.
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Solution Summary
We prove the equality of three matrix norms for a particular type of 2X2 matrix.
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The subordinate matrix norm ||A||_1 is the maximum absolute column sum of A, i.e.
||A||_1 = max(|a|+|b|,|b|+|a|) = |a|+|b|.
Similarly, the subordinate matrix norm ||A||_infinity is the maximum absolute row sum of A, i.e.
||A||_infinity = max(|a|+|b|,|b|+|a|) = |a|+|b|.
The subordinate matrix norm ||A||_2 is given by
||A||_2 = ...
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