Are there any matrix balancing/scaling function in matab for complex rectagular matrices?

I have a complex number matrix with 45 x 2 size. And it needs to be inverted. But the condition number is too large around 8000. So I need to perform matrix balancing to improve the condition number. Is there any function in matlab to perform this operation? I found functions like 'balance', but works only for square matrices.

Answer 1

[Bruno Luong]

Check out normalize

[Bruno Luong]

Here is how to use it

format long
% Generate some unbalance matrix
A=(rand([100,2])+1i*rand([100,2])).*[1e14 1];
y=rand(size(A,1),1);

[An,c,s]=normalize(A);
B = (An+c./s);

cond(A)

ans = 
     1.666924175460802e+14

cond(B)

ans = 
   2.778622490159825

x = (B\y)./s(:) % should be more robust than the following

x = 
  0.000000000000002 - 0.000000000000002i
  0.244040987459613 - 0.184030202199825i

x = A\y

Warning: Rank deficient, rank = 1, tol = 1.825553e+02.

x = 
   1.0e-14 *

  0.409132990480610 - 0.367001236504611i
  0.000000000000000 + 0.000000000000000i

Answer 2

[Steven Lord]

I have a complex number matrix with 45 x 2 size. And it needs to be inverted.

How exactly do you define inversion for a non-square matrix? The standard definition of matrix inverse requires that the matrix be square. There are definitions for generalized inverses; which one are you trying to use?

Or are you trying to solve a system of 45 equations in 2 unknowns? In that case, don't try to invert the matrix. Use the backslash operator instead. As an example with a smaller random coefficient matrix and a known solution of [2; 3]:

rng default % for reproducibility
A = randi([-10 10], 6, 2);
x = [2; 3];
b = A*x;
x2 = A\b % This should be the same as x

x2 = 2×1

2 3

Answer 3

[William Rose]

@Kalasagarreddi Kottakota,

[edit : correct spelling]

You say you want to invert a 45x2 matrix. As you know, a non-square matrix does not have an inverse. But is does have a pseudoinverse. Let us compute G, using the data and the formula from your posting elsewhere:

load g1.mat
load t.mat
G = [g1 -g1.*t];

This particular G is complex, since the data you provided before was complex. Now compute the pseudo inverse:

pinvG=pinv(G);

Confirm that pinvG*G is approximately the identity matrix:

pinv(G)*G

ans = 
   1.0000 - 0.0000i   0.0000 - 0.0000i
  -0.0000 + 0.0000i   1.0000 + 0.0000i

Try it.