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Subsections

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

$\displaystyle y_{i,j} = \overline{a_{j,i}}
$

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
    1.0000000         1.0000000     i     2.0000000        -1.0000000     i  
--> A.'
ans = 
  <complex>  - size: [2 1]
 
Columns 1 to 1
    1.0000000         1.0000000     i  
    2.0000000        -1.0000000     i



Samit K. Basu 2005-03-16