find inverse of a non square binary matrix in matlab

Hi,

I have used a couple of functions to find the inverse of a non-square boolean matrix in matlab. Here is a list of them : using :

      inverse_g=mod(floor(mrdivide(I,A)),2);
      inverse_g=I\A;
      pinv(double(A));
I have tried to verify if the matrix obtained satisfies the property A*inv(A)=inv(A)*A=I

I have found that none of the properties are satisfied. I am not sure because this is a non square matrix if this property still holds good. Since I am using this inverse for processing later on I am sure that the obtained inverse is not correct. Can someone point me to the right direction ?

Thanks, Bhavya

[Image Analyst]

Can you give us the context - the larger picture? Usually when someone says inverse regarding a binary (logical, boolean) matrix, then mean this invertedMatrix = ~logicalMatrix. I don't think you can take the matrix inverse of a non-square matrix, like you are trying to do. That's why I want to know why you think you want to do that.

[Bhavya PH]

I am actually trying to solve the equation Ax=b. In my case both A and b are boolean/logical matrices. I have tried to solve this equation using the

solution=mod(floor(mrdivide(b,A)),2);

But I check this solution it does not seem to match with the values I started with

Answer 1

[Walter Roberson]

Please see http://www.mathworks.com/matlabcentral/answers/16990-galois-field-to-find-the-inverse-of-a-binary-matrix

[Bhavya PH]

Hi,

Thanks for pointing this out to me, this would essentially mean that I would need to use the algorithm implementations to check if a GF(2)matrix is invertible and ten try to invert it in the usual way?

[Walter Roberson]

No, you cannot use the "usual way" to invert it, not if what you want to get out is a boolean matrix. The steps are similar, but you need to interpret '+' as XOR and you need to interpret '*' as AND .