example of linear involution

Let $V$ be the vector space of $m\times n$ complex matrices. Then the operator $L:A\mapsto A^H$, 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
Canonical name	ExampleOfLinearInvolution
Date of creation	2013-03-22 14:14:11
Last modified on	2013-03-22 14:14:11
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	8
Author	mathcam (2727)
Entry type	Example
Classification	msc 15A21
Related topic	BanachAlgebra