(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How do I analytically solve for k to satisfy:

[tex]||kA-I||<1[/tex]?

Here, k is a real number scalar, A is a known matrix.

2. Relevant equations

3. The attempt at a solution

I am confused because if A was a number, I could break it into two cases where kA-I is positive and negative. But now A is a matrix so I can't do so. How should I look at the problem and what other equations are relevant?

Suppose the norm of A is 5, e.g. A = [5 0;0 5]. Then I know that the upper limit of k is 2/5, so that kA-I can be at most [1 0;0 1]. I also know that the lower limit of k has to be 0, because if k is ever negative, the norm would be greater than one, since the norm of I is already 1.

But how do I solve for this kind of result given an arbitrary matrix A?

- Thanks

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# Homework Help: Matrix norm

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