# 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 |
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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 |