正规算子是指内积空间(实的或复的)上与其伴随可交换的算子. 用线性代数的语言描述:设T是内积空间V上的算子,则T是正规的当且仅当.

埃尔米特变换

一个埃尔米特变换满足.由于任何一个算子与它自身都是可交换的,于是所有埃尔米特变换都是正规的.

酉变换

一个酉变换满足,即酉变换与它的伴随互为逆变换.显然酉变换的定义中即说明了它必然是一个正规算子.

In mathematics, especially functional analysis, a normal operator on a complex Hilbert space H is a continuous linear operator N : H → H that commutes with its hermitian adjoint N*, that is: NN* = N*N.

Normal operators are important because the spectral theorem holds for them. The class of normal operators is well-understood. Examples of normal operators are