Mu Analysis and Synthesis Toolbox

Transpose and conjugate transpose of CONSTANT, SYSTEM and VARYING matrices

Syntax

• out = cjt(mat) 
  out = transp(mat) 
  out = vcjt(mat) 
  out = vtp(mat)
  

Description
cjt forms the complex conjugate transpose of the input matrix mat and transpforms the transpose of mat. transp outputs similar results to the MATLAB command .'. These commands also work on SYSTEM and VARYING matrices. For consistency in our naming convention, vcjt and vtp are the same commands as cjt and transp, but work on just CONSTANT and VARYING matrices.

For a SYSTEM matrix mat, transp, and cjt are defined as

Examples
Create a SYSTEM matrix and calculate its transpose and conjugate transpose using cjt and transp.

• A = [-10 0; 0 3]; 
  B = [1 0 3; 0 2 -9]; 
  C = [10 0; 0 4];
  D = [0 -.2 -45; .82 0 .1];
  out = pck(A,B,C,D);
  seesys (out, '%5 .2g')
  
  -10     0   |    1       0       3
   0      3   |    0       2      -9
  --------------------------------------
   10     0   |    0     -.2     -45
   0      4   |     .82    0       .1
  

• x = transp (out);
  seesys (x, '%5 .2g')
  

• -10     0   |    10      0
   0      3   |    0       4
  ---------------------------
   1      0   |    0      .82
   0      2   |   -.2      0 
   3     -9   |   -45     .1
  
  x = cjt(out);
  seesys (x, '%5 .2g')
  

• 10     0   |    -10      0
   0     3   |     0      -4
  ---------------------------
   1     0   |     0      .82
   0     2   |   -.2       0 
   3    -9   |   -45      .1
  
  

Algorithm
These functions call the MATLAB commands ' and .' consistent with the type of input matrices.

See Also
vdiag

blknorm

cmmusyn