# How to find Inverse of a Non-Square Matrix...

• Dec 11th 2009, 12:46 AM
rajez79
How to find Inverse of a Non-Square Matrix...
Hi All,

While doing a DePrecoder for LTE_MIMO, i need to do matrix division. Since matrix division is not possible, i tried to take the inverse of the matrix and multiply it. If it is a square matrix then the above condition will work fine. how to do that for a Non_Square Matrix....??

Ex...,

a = [1 2 3; 4 5 6];
b = [4 5; 2 3; 5 6];

c = a * b;

Now if i want to find matrix b means....

b = c * (1/a) = c * inv(a);

Here inv(c) will not work coz it is not a square matrix. Please help me in finding it.

NOTE : PseudoInverse - pinv() in MATLAB is also not working.
• Dec 11th 2009, 04:18 AM
HallsofIvy
Quote:

Originally Posted by rajez79
Hi All,

While doing a DePrecoder for LTE_MIMO, i need to do matrix division. Since matrix division is not possible, i tried to take the inverse of the matrix and multiply it. If it is a square matrix then the above condition will work fine. how to do that for a Non_Square Matrix....??

Ex...,

a = [1 2 3; 4 5 6];
b = [4 5; 2 3; 5 6];
$\displaystyle a= \begin{bmatrix}1 & 2 & 3 \\ 4 & 5 & 6\end{bmatrix}$
$\displaystyle b= \begin{bmatrix}4 & 2 & 3\\ 5 & 6\end{bmatrix}$

c = a * b;

Now if i want to find matrix b means....

b = c * (1/a) = c * inv(a);

Here inv(c) will not work coz it is not a square matrix. Please help me in finding it.

NOTE : PseudoInverse - pinv() in MATLAB is also not working.[/QUOTE]
A non-square matrix does NOT have an inverse, of course. Your matrix a, above, maps R3 into R2 so obviously, its null space is non-trivial. In this case, its null space is the one dimensional subspace spanned by <1, -2, 1>. That also means that, given a two by two matrix c, there exist an infinite number of two by three matrices, b, such that ab= c.