Moore-Penrose Matrix Inverse 摩尔－彭若斯广义逆 埃尔米特矩阵 Hermitian matrix

 

http://mathworld.wolfram.com/Moore-PenroseMatrixInverse.html

 

 

 

 

显然，埃尔米特矩阵主对角线上的元素都是实数的，其特征值也是实数。对于只包含实数元素的矩阵（实矩阵），如果它是对称阵，即所有元素关于主对角线对称，那么它也是埃尔米特矩阵。也就是说，实对称矩阵是埃尔米特矩阵的特例。

 

https://en.wikipedia.org/wiki/Hermitian_matrix

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j:

  or , in matrix form.

Hermitian matrices can be understood as the complex extension of real symmetric matrices.

If the conjugate transpose of a matrix   is denoted by , then the Hermitian property can be written concisely as

 

Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having real eigenvalues.

 

 

https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse