If matrix A is invertible, is it diagonalizable as well?

Asked Dec 12 '13 at 17:21

Active Dec 12 '13 at 17:24

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If a matrix A is invertible, then it is diagonalizable. Is it true or false?

asked Dec 12 '13 at 17:21

Jane

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True if $A$ is $1\times 1$. – vadim123 Dec 12 '13 at 18:17
@vadim123 It is somewhat meaningless to talk about diagonalizability in $1\times 1$ though... everything is diagonal in $1\times 1$. – Sam Wong Jan 06 '23 at 12:43

1 Answers1

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It is false. Consider $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}$

answered Dec 12 '13 at 17:24

Igor Rivin

26,467

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I love minimal counterexamples. – dfeuer Dec 12 '13 at 17:27