COMP 361 Lecture Notes - Lecture 1: Gaussian Elimination
16 Feb 2016
School
Department
Course
Professor
Document Summary
A = (b) determine the eigenvalues of at a. (c) find kak2. Let a be an n n matrix and let c be the maximum absolute column sum of. Xi=1 (a) prove that for any nonzero vector x rn, we have kaxk1 kxk1. C. (b) show that we can always nd a vector y such that kayk1 kyk1. = c, and conclude that kak1 = c. , yn) are vectors in rn, then the following inequality, called the cauchy-schwartz inequality, is always true: xiyi!2 n. Using the cauchy-schwartz inequality, prove that kx + yk2 kxk2 + kyk2 (this is the triangle inequality for the two-norm). Use gaussian elimination to nd the lu-decomposition of the matrix. Let f be the vector (4, 8, 7)t . Using the matrices l and u you found, solve lg = f for g then solve ux = g for x.
