ThmDex – An index of mathematical definitions, results, and conjectures.

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Result R5586 on D5870: Invertible complex matrix

Diagonalizable complex matrix need not be invertible

Formulation 0

Let

$A \in \mathbb{C}^{2 \times 2}$ be a D6159: Complex square matrix such that

(i)	$\begin{equation} A = \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix} \end{equation}$

Then

(1)	$A$ is a D5676: Diagonalizable complex matrix
(2)	$A$ is not an D5870: Invertible complex matrix

Also known as

Counterexample: complex square matrix which is diagonalizable but not invertible