矩阵的转置共轭就是厄米变换

conjugate transpose, Hermitian transpose, or adjoint matrix of an m-by-n matrix A with complex entries is the n-by-m matrix A^* obtained from A by taking the transpose and then taking the complex conjugate of each entry. The conjugate transpose is formally defined by

where the subscripts denote the i,j-th entry, for 1 ≤ i ≤ n and 1 ≤ j ≤ m, and the overbar denotes a scalar complex conjugate. (The complex conjugate of a + bi, where a and b are reals, is a − bi.)

This definition can also be written as

where denotes the transpose and denotes the matrix with complex conjugated entries.

Other names for the conjugate transpose of a matrix are Hermitian conjugate, or transjugate. The conjugate transpose of a matrix A can be denoted by any of these symbols:

• or , commonly used in linear algebra
• , universally used in quantum mechanics