Idempotent matrix

In algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix M is idempotent if and only if MM = M. For this product MM to be defined, M must necessarily be a square matrix. Viewed this way, idempotent matrices are idempotent elements of matrix rings.

Examples of a ${\displaystyle 2\times 2}$ and a ${\displaystyle 3\times 3}$ idempotent matrix are ${\displaystyle {\begin{bmatrix}1&0\\0&1\end{bmatrix}}}$ and ${\displaystyle {\begin{bmatrix}2&-2&-4\\-1&3&4\\1&-2&-3\end{bmatrix}}}$, respectively.

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