Conjugate transpose
Conjugate transpose is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Suppose that a matrix contains complex numbers. Then the conjugate transpose of is a matrix containing the complex conjugates of the matrix transposition of .
This means that row , column of the conjugate transpose equals the complex conjugate of row , column of the original matrix.
In the next list, must also be a square matrix.
- A Hermitian matrix equals its own conjugate transpose: .
- A normal matrix is commutative in multiplication with its conjugate transpose: .
- A unitary matrix has its inverse equal to its conjugate transpose: . This is true iff and iff , where is the identity matrix.
Given some matrix of complex numbers, find its conjugate tranpose. Also determine if it is a Hermitian matrix, normal matrix, or a unitary matrix.
- MathWorld: conjugate transpose, Hermitian matrix, normal matrix, unitary matrix