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