MATH 307 Study Guide - Midterm Guide: Power Iteration, Matrix Norm, Block Matrix

• School: UBC
• Department: Mathematics
• Course: MATH 307
• Professor: all

Document Summary

A matlab/octave formula sheet is provided on the last page. [12] 1. (a) [3 pts] write down the de nition of the matrix norm kak of a matrix a. (b) [3 pts] write down the de nition of the condition number cond(a) of a matrix a. Why is this a useful concept? (c) [3 pts] if a is a 2 2 matrix with kak = 2, is it possible that a(cid:20)1. Give a reason. (d) [3 pts] find the norm and condition number of (cid:20)0 2. [15] 2. (a) [2 pts] write down the de nition of a hermitian matrix. (b) [3 pts] true or false: eigenvectors for distinct eigenvalues are orthogonal for a real symmetric matrix. Justify your answer. (c) [3 pts] true or false: if a square matrix has repeated eigenvalues, then it cannot be diagonalized. Assume that a and n have been de ned in matlab/octave, and that the size of a is.