“Hermitian Matrix”的概念、定义、习题解题方法及翻译-数学辞典

单词

Hermitian Matrix

释义

Hermitian Matrix

If a Matrix is Self-Adjoint, it is said to be a Hermitian matrix. Therefore, aHermitian Matrix is defined as one for which

(1)

where

denotes the Adjoint Matrix. Hermitian Matrices have RealEigenvalues with Orthogonal Eigenvectors. ForReal Matrices, Hermitian is the same as symmetrical. Any Matrix

which is not Hermitian can be expressed as the sum of two Hermitian matrices

(2)

Let

be a Unitary Matrix and

be a Hermitian matrix. Then the Adjoint Matrix of aSimilarity Transformation is


			(3)

The specific matrix

(4)

where

are Pauli Spin Matrices, is sometimes called ``the'' Hermitian matrix.

See also Adjoint Matrix, Hermitian Operator, Pauli Spin Matrices

References

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

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