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 = 
  <int32>  - size: [2 3]
 
Columns 1 to 3
          1           2           0  
          4           1          -1  
--> A'
ans = 
  <int32>  - size: [3 2]
 
Columns 1 to 2
          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 = 
  <complex>  - size: [1 2]
 
Columns 1 to 2
   1+  1 i    2 -1 i  
--> A.'
ans = 
  <complex>  - size: [2 1]
 
Columns 1 to 1
   1+  1 i  
   2 -1 i