MATH 415 Study Guide - Final Guide: Orthogonal Matrix, List Of Trigonometric Identities, Matrix Multiplication

• School: University of Illinois
• Department: Mathematics
• Course: MATH 415
• Professor: J Li

Document Summary

Computations: (1) find the fourier coe cients a0, a1, b1, a2, b2 of the function f (x) =(1 x [0, 2 ] otherwise. 0: decide if the following matrices are positive de nite, negative de nite or inde nite (cid:3) a0 = 1 (1) a = (2) b = (3) c = (1) det[2] = 2, det(cid:20) 2 2 (2) det[2] = 2 > 0, det(cid:20) 2 1. We use the leading minors test on the rst 2. 2 = 0 so a is not de nite. They are all positive (3) note that the columns of the matrix shown are independent, since the matrix is sym- metric this means its eigenvalues are non-zero real numbers. Since c is the square of that matrix, its eigenvalues are squares of the previous eigenvalues and therefore are all positive. Tutoring room hours: monday 4-8pm, tuesday 6-8pm, wednesday 5-7, thursday 4-6. 1 (cid:3: consider the matrix a =(cid:20)1 b.