Matrix inverse for non-square matrix

I am trying to create a code that solves viscoelastic mechanical behavior problems using the collocation method. In order to do this I need to solve the following;

[A]{D}={B} where is D is the array needing to be solved. Therefore {D}=[A]^-1 {B} where A is a (j x k) matrix and B is a (k x 1) array making the resulting D a (j x 1) array. In my current code j = 11 and k = 1,400,000. I've tried the following codes but the results are not correct;

Dj = pinv(Akj).*Bk;

However, this results in a k x j matrix for D.

and;

Dj = (Akj.^(-1))*Bk;

Which does result in the correct j x 1 array for D, but I do not believe it is given the correct values.

Thank you for your time.

[David Goodmanson]

Hi John,

If A is (j x k) then D has to be (k x 1) and B is (j x 1). Do you mean that A is (k x j)?

[David Wilson]

If A is (j*k), however that is less likely given that A then is "short and wide".

In any case, a better computational approach is never to compute the inverse explicitly, but rather use "backslash",

D = A\B

Read the help on mldivide.

If A is sparse, you might want to take advantage of that.

[Christine Tobler]

I agree with David, probably the best would be to just use backslash.

Also, in your call

pinv(Akj).*Bk

the .* operator does an elementwise multiplication, not a matrix multiplication as you were probably intending.

The inv function errors for non-square matrices, so it should just not work, not give you any wrong results.

[John Chesser]

As mentioned above, A is supposed to be a (k x j) matrix. When filling A with it's values I had isssues in my loops which were causing A to be a (j x k) matrix. I have since fixed this and have implemented the suggested D = A\B, and it is working correctly and giving correct solutions. Thank you all for your help!