Normal Endomorphism

Definition

That is to say $E$ a Space préhilbertien, reality or complex. That is to say $U$ a endomorphism of $E$ admitting an assistant $u^*$. it is said that $U$ is normal if and only if $U\; \backslash \; circ\; u^*=u^*\; \backslash \; circ\; u$.

Examples

• the endomorphisms autoadjoints are normal.
• the automorphism orthogonal are normal.

Properties

• When $E$ is a square Espace, a endomorphism of $E$ is normal if and only if it is diagonalisable in orthonormée base.
• Attention, in the real case, in fact the endomorphisms autoadjoints are diagonalisables in orthonormée base.

Random links:

Celine Montaland | Haramachi | Israeli-Arab war of 1948 | 9K32 Strela-2 | Dorothy Stevenson | Pulau_Brani

© 2007-2008 speedlook.com; article text available under the terms of GFDL, from fr.wikipedia.org