05242016 01:30 PM
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

05242016 02:11 PM
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} / (adbc);
So you can see that if all the original elements are positive, then exactly two of the elements in the inverse must be negative.
05242016 01:37 PM
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.
05242016 01:56 PM
Thanks. I am not clear for some parts. Why I get negative numbers for inv?
05242016 02:11 PM
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} / (adbc);
So you can see that if all the original elements are positive, then exactly two of the elements in the inverse must be negative.
Need further help from the community? Please ask a new question.