Suppose is nilpotent. Prove that is invertible. So . Then which implies that is invertible. Is this correct?
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Ok let which converges. So . And so .
Originally Posted by manjohn12 Suppose is nilpotent. Prove that is invertible. So . Then which implies that is invertible. Is this correct? if then
Originally Posted by manjohn12 Suppose is nilpotent. Prove that is invertible. So . Then which implies that is invertible. Is this correct? What is the reason for"So . Then " ... I mean what is the reason to assume det(A+I) = 1? Since the matrix is nilpotent, its characteristic polynomial is . So , now put , we get , thus A+I is invertible. Oops! looks like you have already answered the question
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