# example of linear involution

Let $V$ be the vector space of $m\times n$ complex matrices. Then the operator $L\colon A\mapsto A^{H}$, which takes a matrix $A\in V$ into its Hermitian conjugate $A^{H}\in V$ is an involution. The projection operators induced by this involution decompose a matrix into a direct sum of Hermitian and skew-Hermitian matrices.

Title example of linear involution ExampleOfLinearInvolution 2013-03-22 14:14:11 2013-03-22 14:14:11 mathcam (2727) mathcam (2727) 8 mathcam (2727) Example msc 15A21 BanachAlgebra