Thread Subject: Inverse of a matrix

Hi All,

I want to get the inverse of a matrix. For example, if the matrix is
PSF =(1/16)* [1 2 1; 2 4 2;1 2 1];
and if I call
chck_inv_PSF = inv(PSF);
this returns a matrix with values as infinity. But if I get the
inverse as a division by the identity matrix, i.e.
PSF_size =[3,3];
inv_PSF = eye(PSF_size(1), PSF_size(2))./PSF;
Then it will return a matrix with values in the diagonal.
16 0 0
0 4 0
0 0 16.

Which one is correct? Am I doing anything wrong?

Thanks in advance for all the help.

Dev

Dev <gunadp@yahoo.com> wrote in message
<be763f10-6c53-46bc-8eec-624e52024a89@i18g2000prn.googlegroups.com>...
> Hi All,
>
> I want to get the inverse of a matrix. For example, if the
matrix is
> PSF =(1/16)* [1 2 1; 2 4 2;1 2 1];
> and if I call
> chck_inv_PSF = inv(PSF);
> this returns a matrix with values as infinity. But if I
get the
> inverse as a division by the identity matrix, i.e.
> PSF_size =[3,3];
> inv_PSF = eye(PSF_size(1), PSF_size(2))./PSF;
> Then it will return a matrix with values in the diagonal.
> 16 0 0
> 0 4 0
> 0 0 16.
>
> Which one is correct? Am I doing anything wrong?
>
> Thanks in advance for all the help.
>
> Dev

Hi Dev

The first result is OK. Why? Your matrix is singular, which
has no finite inverse. Its rang is one, because the first
and last rows are the same and second row is only doubled
first row.
Why your second attempt gave finite results? The operation
you used was not an inverse, but only an array division
(term by term).

Mira

Dev <gunadp@yahoo.com> wrote in message <be763f10-6c53-46bc-8eec-
624e52024a89@i18g2000prn.googlegroups.com>...
> Hi All,
>
> I want to get the inverse of a matrix. For example, if the matrix is
> PSF =(1/16)* [1 2 1; 2 4 2;1 2 1];
> and if I call
> chck_inv_PSF = inv(PSF);
> this returns a matrix with values as infinity. But if I get the
> inverse as a division by the identity matrix, i.e.
> PSF_size =[3,3];
> inv_PSF = eye(PSF_size(1), PSF_size(2))./PSF;
> Then it will return a matrix with values in the diagonal.
> 16 0 0
> 0 4 0
> 0 0 16.
>
> Which one is correct? Am I doing anything wrong?

rank will show your matrix to be singular.

You cannot form a finite inverse for a
singular matrix.

You should not be using inv in the first
place. There are far better choices almost
always. Just because the formula in your
book shows a matrix inverse, it is usually
incorrect to implement that formula as
written with an inverse. Instead, use
either matlab's backslash operator, or
the pinv function.

John