MATH235 Study Guide - Final Guide: Orthogonal Matrix, Triangular Matrix, Symmetric Matrix

• School: University of Waterloo
• Department: Mathematics
• Course: MATH235
• Professor: Ghazal Geshnizjani

Document Summary

Due: wednesday nov 4th: for each of the following symmetric matrices, nd an orthogonal matrix p and diagonal matrix d such that p t ap = d. 2 6(cid:21) (a) a = (cid:20)6 2 (b) a = (c) a = . Find an orthogonal matrix p and upper triangular matrix t such: prove that if a is an n n symmetric matrix, then there exists an n n symmetric matrix. B such that b 3 = a: prove that every n n matrix a with real eigenvalues is orthogonally similar to a lower triangular matrix t , determine whether each statement is true or false.