# How to obtain the value of the matrix X in equation AXA' = B?

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If I have

A*X*A' = B

X and B are real square matrices.

A might not be square matrix.

For example:

A (3x4) is given

B (3x3) is given

X (4x4) is unknown matrix.

How can I obtain the X matrix?

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### Accepted Answer

KSSV
on 18 Jan 2022

For the give dimensions and given equation it cannot be solved. But for given dimensions the following equation can be solved.

% A'*X*A = B

To solve above A can be (3x4) , X is (3,3) abd B is (4x4).

A = rand(3,4) ;

B = rand(4,4) ;

X = pinv(A')*B*pinv(A)

If you want to solve the given equation:

% A*X*A' = B

The dimensions of A should be (4x3), X is (3x3) and B is (4X4)

A = rand(4,3) ;

B = rand(4,4) ;

X = pinv(A)*B*pinv(A')

Check the dimensions once for your quesion. Read about pinv function and it's properties.

### More Answers (1)

Torsten
on 18 Jan 2022

Edited: Torsten
on 18 Jan 2022

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