Let T be a square matrix and I be the corresponding Identity Matrix. Show that if is sufficiently small, there exists a linear Operator S such that . Hint: expand log(1+x) in a Taylor series.
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Originally Posted by EinStone Let T be a square matrix and I be the corresponding Identity Matrix. Show that if is sufficiently small, there exists a linear Operator S such that . Hint: expand log(1+x) in a Taylor series. Let , and suppose that . Then define . The series converges absolutely, because and that series has radius of convergence 1. Then .
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