“Unitary Matrix”的概念、定义、习题解题方法及翻译-数学辞典

单词

Unitary Matrix

释义

Unitary Matrix

A unitary matrix is a Matrix for which

(1)

where

denotes the Adjoint Operator. This guarantees that

(2)

Unitary matrices leave the length of a Complex vector unchanged. The product of two unitary matrices is itself unitary.If

is unitary, then so is

. A Similarity Transformation of a Hermitian Matrix witha unitary matrix gives


			(3)

For Real Matrices, Hermitian is the same as Orthogonal. Unitary matrices are Normal Matrices.

If is a unitary matrix, then the Permanent

(4)

(Minc 1978, p. 25, Vardi 1991).

See also Adjoint Operator,Hermitian Matrix, Normal Matrix, Orthogonal Matrix, Permanent

References

Arfken, G. ``Hermitian Matrices, Unitary Matrices.'' §4.5 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 209-217, 1985.

Minc, H. Permanents. Reading, MA: Addison-Wesley, 1978.

Vardi, I. ``Permanents.'' §6.1 in Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, pp. 108 and 110-112, 1991.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。