Lecture23filled

Lecture23filled - University of Toronto at Scarborough...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: University of Toronto at Scarborough Department of Computer 85 Mathematical Sciences MAT W inter 2008 Lecture 23 Similar Matrices Sophie Chrysostomou DEFINETION 0.1 If A, B are n X n matrices such that B :- P“1AP for some invertible n X 71 matrix P, then we say that A and B are similar mairices. rm down that A , P7 0% diggonahzaHe. LEMMA 0.2 If A and B are similar, than IA] 2 lBl. VLF: A)V7 I :73 Invarin F Ski» F"AP=E7 :7 Maw-‘Amaw-‘y \M. m= “'9‘; l M mam LEMMA 0.3 I f A and B are similar, than A and B have the 35mm eigenmhws. \‘5"3\1\5\P“‘AP’M”‘VI == P"(APu-M)|=IV"‘<A«)\1)P\ Wort/mes awe NUT wit-lawn»?! mwﬁm = m'mmll vi =\'A~J\1\ [97»in Hivmi A, {5 have the, gym/«L eigmvaluzy E THEOREM 0.4 The Cayley~Hamilton Theorem: Let/1 be an mm matm with, characteristic polynomial 300) m ] AMA] l :2 an)? + ammmml +- - -~1~ (mm-Hm, then p(A)=anA”+anm1A”"i+---+a.1A+a01=0 0 mm matrix. 2 0 3. 1 Howe/work 3 5 4 1 mmwg'g A: “4 m3 —3 w1 1 0 1 2 2"“. M212 ‘1 A: 020' A’AI: O "‘ " :2’N ‘ O ‘l\10 l ‘ *} iz-‘Ao ( 013‘ o 002 "‘ ‘ 2’)‘ gnaw-(’sz >- (1-00” = (100” :— ﬁ'w—gﬁ—ntyﬂ» azx—M, ‘53 C—H Thm: A“; 23 WﬂQA’WvA +1 b1:- 04,” IL 1:: ~ Ans A114 PH‘yz A :W —| leCA*+—.§_A"-~};A‘+1IX .. 'v "7 ~(‘7‘ng"+%A ~ 33A+Z]) A .4 liver?» 4‘0er 200! :0 a 3'71; <7 23 0’17, +«é u 4ov\$wéf1°4+1 I “WW—3 “i7. -lf_(+ (1...; I‘lo 0 I 0 0 0 g a 6) (9 Li- 0 0 0L I V1 O V’l/Lé “Tth Emmi) W is diqﬂonalizab‘c. Nita—JR , 2 ...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

Lecture23filled - University of Toronto at Scarborough...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online