HERMITIAN Matrix Hermitian (Conjugate Transpose) Operator

Usage

Computes the Hermitian of the argument (a 2D matrix). The syntax for its use is

  y = a';

where a is a M x N numerical matrix. The output y is a numerical matrix of the same type of size N x M. This operator is the conjugating transpose, which is different from the transpose operator .' (which does not conjugate complex values).

Function Internals

The Hermitian operator is defined simply as

where y_ij is the element in the ith row and jth column of the output matrix y.

Examples

A simple transpose example:

--> A = [1,2,0;4,1,-1]

A = 

  1  2  0 
  4  1 -1 

--> A'

ans = 

  1  4 
  2  1 
  0 -1

Here, we use a complex matrix to demonstrate how the Hermitian operator conjugates the entries.

--> A = [1+i,2-i]

A = 

    1.0000 +  1.0000i    2.0000 -  1.0000i 

--> A.'

ans = 

    1.0000 +  1.0000i 
    2.0000 -  1.0000i