# anti-idempotent

An element $x$ of a ring is called an anti-idempotent element, or simply an anti-idempotent if $x^{2}=-x$.

The term is most often used in linear algebra. Every anti-idempotent matrix over a field is diagonalizable. Two anti-idempotent matrices are similar if and only if they have the same rank.

Title anti-idempotent Antiidempotent 2013-03-22 13:47:22 2013-03-22 13:47:22 mathcam (2727) mathcam (2727) 4 mathcam (2727) Definition msc 16U99 LinearInvolution