Idempotency
Idempotency refers to any process that has the same outcome whether operated once or many times.
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Description
An idempotent matrix can be multiplied by another matrix any number of times and the product of the first operation is returned every time. More simply put, an idempotent matrix can be raised to any power and still be equal to the original: A2 = A.
For example, the projection matrix P is characterized as H(HTH)-1HT. If this were squared to H(HTH)-1HTH(HTH)-1HT, then per the core principle of inversion (i.e., AA-1 = I), half of the terms would cancel out. P2 = P.
Only a square matrix can be idempotent.