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

If T is a linear transformation on R^n with || T-I || < 1, prove that T is invertible.

3. The attempt at a solution

So a linear transformation T is invertible iff the matrix T is not singular.

and I know for any matrix A, ||A|| > spectral radius(A).

so, spectral radius(T-I) < 1.

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# Invertible linear transformation

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