problem with inversion of a matrix

Hi, I need to do an inversion of N=(B*(R)^(-1)*B')^(-1). B->12x4 R->4x4, as a result my matlab gives me matrix 1x1. The problem is the last inversion, because without it as a result is matrix 12x12. Could anyone help me?

[Stephen23]

You need to read this:

https://www.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html

and then review the operations that you are using.

[Torsten]

There must be something wrong in your definition of N. B is (12x4), R^(-1) is (12x12). Thus B*R^(-1) is not defined ...

Please show the MATLAB code you are using at the moment.

Best wishes

Torsten.

[Paulina Superczynska]

Torsten, I've made a mistake while writting, matrix R is 4x4.

[Torsten]

As written, the inverse of N is

N^(-1) = B*(R)^(-1)*B'

Do you have problems computing this matrix ?

Best wishes

Torsten.

[Paulina Superczynska]

I need to compute (B*(R)^(-1)*B')^(-1), it is not a problem to compute B*(R)^(-1)*B', but when I try to use inversion on final matrix I don't get matrix 12x12.

[John D'Errico]

READ MY ANSWER! You don't get an inverse, because the inverse of a singular matrix does not exist. Just wanting to compute something that does not exist is a problem, and a problem that cannot be solved. At best you can compute a pseudo-inverse.

Answer 1

[John D'Errico]

So what is the problem? Let me guess, the inverse you are trying to compute does not exist?

You state:

N=(B*(R)^(-1)*B')^(-1). B->12x4 R->4x4

The intermediate result of

B*(R)^(-1)*B'

is indeed a 12x12 matrix. But it is a matrix that has rank 4 at the very most. That is a given (linear algebra 101).

The inverse of a 12x12 rank 4 matrix does not exist. The matrix is singular, and a singular matrix has no inverse.

So for whatever reason you think you need to do this, you are wrong.

We don't know what the purpose of this expression you are trying to compute. Can a pseudo-inverse (help pinv) satisfy your needs? How can we know? The one thing that I do know is that trying to compute the inverse is not going to be a success.