Recent content by Vai

Homework Statement x,y, z are vectors in R^n. We have the equation: ax +by +cz, where a,b,c are constants such that a+b+c=1, and a,b,c>=0 What is the geometric interpretation of the equation? Homework Equations sv + tu, where u,v are vectors in R^n and s,t are constants such that...

Ok, thank you very much for your help; saved me a lot of time there.

Whoops, I'm really sorry. I had to prove that the absolute value of the determinant of A is equal to the product of the singular values. then: |det(A)| = |det(U) * det(E) * det(V)| = | (+/- 1) * (product of singular values) * (+/- 1) | = product of singular values

Thanks for the quick response. I'm not sure about the sign on the singular values. Since they are the square roots of the eigenvalues of A' * A, then I assume that they are all positive. So then that means det(E) is also positive. I wasn't aware that U and V are unitary matrices. But your...

Homework Statement So I'm working on this proof. Given an n x n (square) matrix, prove that it's determinant is equal to the product of it's singular values. Homework Equations We are given A = U*E*V as a singular value decomposition of A. The Attempt at a Solution I was thinking that...