this is my first question on this website. I'm looking at a Matlab problem, and don't seem to know how to do it. Before I type the question, I want to make it clear that I'm looking for an UNDERSTANDING, NOT an ANSWER. Although, I must admit, I won't be angry if an answer is posted. But more importantly, I need to understand this.
"The matrix factorization LU = PA can be used to compute the determinant of A. We have
det(L)det(U) = det(P)det(A).
Because L is triangular with ones on the diagonal, det(L) = 1. Because U is triangular, det(U) = u 11 u 22 · · · u nn . Because P is a permutation, det(P) = +1 if the number of interchanges is even and −1 if it is odd. So det(A) = ±u 11 u 22 · · · u nn .
Modify the lutx function so that it returns four outputs.
function [L,U,p,sig] = lutx(A)
%LU Triangular factorization
% [L,U,p,sig] = lutx(A) computes a unit lower triangular
% matrix L, an upper triangular matrix U, a permutation
% vector p, and a scalar sig, so that L*U = A(p,:) and
% sig = +1 or -1 if p is an even or odd permutation.
Write a function mydet(A) that uses your modified lutx to compute the determinant of A. In Matlab, the product u 11 u 22 · · · u nn can be computed by the expression prod(diag(U))."`
The lutx code can be found here:
I'm having difficulty understanding the concept of the problem, and also the code that needs to be written. Any help would be very appreciated. Thank you.
