1381170045_768__232_lecture_4.4

# 4 notesspeaker eigenvalues and eigenvectors 1 sept 7

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Unformatted text preview: S: Part A.1, A.2 Comtet74 Handout #1 (self study) Symbolic methods Combinatorial parameters FS A.III (self-study) Combinatorial Parameters Analytic Methods FS: Part B: IV, V, VI Appendix B4 Stanley 99: Ch. 6 Handout #1 (self-study) Complex Analysis Unlabelled structures Deﬁnition. If A is a square matrix, then a scalar λ is a called an eigen3 21 II.1, II.2, II.3 Labelled structures I 4 28 II.4, A II.6 there is some vector x = 0 such that II.5, if Labelled structures II value of 5 Oct 5 III.1, III.2 6 12 IV.1, IV.2 7 19 IV.3, IV.4 Multivariable GFs Asst #1 Due Ax = λx Singularity Analysis If λ is an V.1 eigenvalue of a square matrix A, then any nonzero vector x that IV.5 9 Nov 2 Asst #2 Due Asymptotic methods satisﬁes 9 VI.1 Sophie 10 Ax Mariolysx =λ 12 A.3/ C Introduction to Prob. 8 26 18 Limit is calledIX.1 eigenvector of Laws corresponding to eigenvalue λ. an A and Comb Marni 11 20 IX.2 23 IX.3 13 30 IX.5 14 Dec 10 Random Structures and Limit Laws FS: Part C (rotating presentations) Discrete Limit Laws Sophie Combinatorial Mariolys instances of discrete 2 1 3 Example. Is an eigenvector of Marni ? 25 IX.4 Continuous Limit Laws 1 3 −6 12 Quasi-Powers and Gaussian limit laws Presentations Sophie Asst #3 Due Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY Version of: 11-Dec-09 Is 3 23 an eigenvector of ? 1 3 −6 C EDRIC C HAUVE , FALL 2013 3 MATH 895-4 Fall 2010 Course Schedule f a cu lty of science d epa r tm ent of m athema tic s Week Date 1 Sept 7 Sections Part/ References Findingfrom FS2009 Eigenvalues. I.1, I.2, I.3 Topic/Sections Combinatorial Structures FS: Part A.1, A.2 Comtet74 Handout #1 (self study) Combinatorial Parameters Analytic Methods FS: Part B: IV, V, VI Appendix B4 Stanley 99: Ch. 6 Handout #1 (self-study) Notes/Speaker Symbolic methods Combinatorial parameters FS A.III (self-study) MATH 232 S ECTION #4.4 Complex Analysis 2 14 I.4, I.5, Unlabelled Recall that I.6 eigenvalue λ of astructures an square matrix A is a scalar such that 3 21 II.1, II.2, II.3 4 28 II.4, II.5, II.6 5 Oct 5 III.1, III.2 6 12 IV.1, IV.2 7 19 IV.3, IV.4 8 26 9 Nov 2 Labelled structures I Labelled structures II Asst #1 Due Multivariable GFs has a nontrivial solution.Singularity Analysis IV.5 V.1 Asymptotic methods Asst #2 Due VI.1 This9 will happen if and only if λI − ASophie is 10 12 A.3/ C Introduction to Prob. Mariolys 18 IX.1 Limit Laws and Comb Marni 20 IX.2 Discrete Limit Laws Sophie 23 IX.3 Combinatorial instances of discrete Mariolys 25 IX.4 Continuous Limit Laws Marni 13 30 IX.5 Quasi-Powers and Gaussian limit laws Sophie 14 Dec 10 11 12 Random Structures and Limit Laws FS: Part C (rotating presentations) Presentations Example. Find the eigenvalues of Asst #3 Due 23 . 3 −6 Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY Version of: 11-Dec-09 C EDRIC C HAUVE , FALL 2013 4 MATH 895-4 Fall 2010 Course Schedule f a cu lty of science d epa r tm ent of m athema tic s Week Date Sections 1 Sept 7 I.1, I.2, I.3 2 14 I.4, I.5, I.6 3 21 II.1, II.2, II.3 Part/ References Topic/Sections MATH 232 S ECTION #4.4 Notes/Speaker from FS2009 Deﬁnition. For an n × n matrix A, the polynomial of degree n in λ given by Combinatorial Structures FS: Part A.1, A.2 Comtet74 Handout #1 (self study) Symbolic methods Combinatorial parameters FS A.III (self-study) Combinatorial Parameters Unlabelled structures p(λ) = det(λI − A) Labelled structures I 4 28 Labelled structures II is calledII.4, II.5, II.6characteristic polynomial of A. the 5 Oct 5 III.1, III.2 6 12 IV.1, IV.2 Asst #1 Due Multivariable GFs So, for example, weMethods found the characteristic polynomial of 7 19 IV.3, IV.4 Complex Analysis Analyti...
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## This note was uploaded on 12/08/2013 for the course MATH 232 taught by Professor Russel during the Fall '10 term at Simon Fraser.

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