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I would like to know what is a idempotent matrix? Also, which invertible matrices are also idempotent and can a matrix be nilpotent and idempotent at the same time?

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  1. In algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself. (guess where this is from...)

  2. With the exception of the identity matrix, an idempotent matrix is singular...

  3. Does the zero matrix count?

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In fact, there are exactly three kinds of idempotant matrices: the unit matrix (invertible), the zero matrix (nilpotent) and all others (neither). – Johannes Kloos Oct 9 '12 at 9:17

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