MAT224H1 Study Guide - Final Guide: Orthogonal Complement, Diagonal Matrix, Diagonalizable Matrix
Document Summary
A brief summary of material since test 2. Below is a very brief summary of the main concepts covered during the tuesday april 14 review session. For more details, please see your lecture notes or the textbook. Also, note that the abbreviation tp is short for tutorial problems . Let v be a nite dimensional vector space over a eld f , and let t : v v be a linear map. Recall: f is an eigenvalue of t (defn) x (cid:54)= 0 such that t (x) = x. (thm) is a root of the characteristic polynomial p(t) = det(t ti). Recall: x v is an eigenvector of t with eigenvalue f (defn) x (cid:54)= 0 and t (x) = x. (thm) x (cid:54)= 0 and x ker(t i). Recall: the -eigenspace of t is e = {x v | t (x) = x}.
