topic Re: call inv in SAS/IML Software and Matrix Computations

call inv

Bal23 — Tue, 24 May 2016 17:30:18 GMT

b={4 9, 16 25, 36 49};

x={7 5, 16 9};

a=sqrt(b); * Assign square root of each element of B to corresponding element of A;

y=inv(x); * Call INV function to compute inverse matrix of X and assign results to Y;

r=rank(x);

I do not know how inv is calculated. I do not know how I can get the follow numbers. Can you explain the function of inv?Thanks.

-0.529412

0.2941176

0.9411765

-0.411765

Re: call inv

Rick_SAS — Tue, 24 May 2016 17:37:28 GMT

If Y is the inverse matrix of X, then Y*X = I, where I is the identity matrix that has 1s on the diagonal and 0s off the diagonal.

The inverse matrix is used to solve matrix equation. For example, if you are given a square nxn matrix A and and an nx1 vector w, then you might want to know if there is a vector v such that

A*v = w

Under certain conditions, the solution is the vector v = inv(A)*w.

Re: call inv

Bal23 — Tue, 24 May 2016 17:56:35 GMT

Thanks. I am not clear for some parts. Why I get negative numbers for inv?

Re: call inv

Rick_SAS — Tue, 24 May 2016 18:11:21 GMT

Because the negative values are required so that X*inv(X) = I.

Since your example is a 2x2 matrix, there is even a formula for the inverse. for any numbers a,b,c, and d, define the matrix

A = {a b, c d};

Then

inv(A) = {d -b, -c a} / (ad-bc);

So you can see that if all the original elements are positive, then exactly two of the elements in the inverse must be negative.