STAT444 Study Guide - Winter 2019, Comprehensive Final Exam Notes - Positive-Definite Matrix, Knot, Yi I

• School: University of Waterloo
• Department: Statistics
• Course: STAT444
• Professor: Kun Liang

Document Summary

Notation8 aix 0 capital letters are matricesvectors a x e lowercase letters are scalers underlinelower cases are vectors g xu vector is a matrixwith 1 column i e a column vector. 1 supposea caijoan is symmetric i. e aij aji i row. Then f ytay j col tf i j a yitj is a quadraticform. Ii ai trcan m trcbd tr cb sum of diagonal elements. 3 rank rankcat is the max columns or rows of a of linearly independent. 4 a non zero vectorui is an eigenvector ofanan if t cnyn o. Afi whenxi b the corresponding ith eigenvalue ie b n. 5 a matrix it is idempotent if aa a. Result1 if his idempotentthen all its eigenvalues are either o or l. If a is idempotent then there exists an orthogonalthatrixp suchthat it papt where a l a eigenvalues being 1. Matrixform ns ci in short y xp t e it.