1381170045_768__232_lecture_4.4

1 sophie 10 ues 12 a3 c entries on the main prob

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Unformatted text preview: A.1, A.2 Comtet74 Handout #1 (self study) Symbolic methods Analytic Methods FS: Part B: IV, V, VI Appendix B4 Stanley 99: Ch. 6 Handout #1 (self-study) Complex Analysis Unlabelled structures 123 4 28 II.4, II.5, II.6 Labelled structures For our upper triangular matrix A II= 0 4 7, the eigenvalues (listed with Combinatorial Combinatorial 5 Oct 5 III.1, III.2 Asst 0 Due #1 0 1 parameters Parameters FS A.III multiplicity) are 1, 1, and 4. 6 12 IV.1, IV.2 Multivariable GFs (self-study) 3 21 II.1, II.2, II.3 7 19 IV.3, IV.4 Note that V.1 A) = det( IV.5 8 26 9 Nov 2 and 9tr(AVI.1= ) 10 12 A.3/ C Labelled structures I Singularity Analysis Asymptotic methods Asst #2 Due Sophie Introduction to Prob. Mariolys 18 IX.1 Limit Laws and So for upper triangular matrices,Comb Marni the determinant is 11 Random Structures 20 IX.2 23 IX.3 25 IX.4 13 30 IX.5 14 Dec 10 12 Discrete Limit Laws Sophie Combinatorial instances of discrete Mariolys Continuous Limit Laws Marni Quasi-Powers and Gaussian limit laws and Limit Laws FS: Part C (rotating presentations) Sophie Presentations Asst #3 Due and the trace is Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY Version of: 11-Dec-09 The same principle holds for lower triangular and diagonal matrices. C EDRIC C HAUVE , FALL 2013 16 f a cu lty of science d epa r tm ent of m athema tic s Week Date Sections from FS2009 1 Sept 7 I.1, I.2, I.3 2 14 I.4, I.5, I.6 Part/ References 9 2 × 2 Matrices 9.1 3 4 5 If 6 7 21 Topic/Sections MATH 232 S ECTION #4.4 Notes/Speaker Symbolic methods Unlabelled structures Eigenvalues of 2 × 2 Matrices II.1, II.2, II.3 Labelled structures I 28 II.4, II.5, II.6 Labelled structures II Combinatorial Combinatorial aOct 5b III.1, III.2 p Parameters is a 2 ×arameters 2 matrix, then FS A.III c12 d IV.1, IV.2 Multivariable GFs (self-study) 19 IV.3, IV.4 det(A) = 8 26 9 Combinatorial Structures FS: Part A.1, A.2 Comtet74 Handout #1 (self study) MATH 895-4 Fall 2010 Course Schedule Nov 2 9 tr(A) = 10 12 IV.5 V.1 VI.1 Analytic Methods FS: Part B: IV, V, VI Appendix B4 Stanley 99: Ch. 6 Handout #1 (self-study) A.3/ C Asst #1 Due Complex Analysis Singularity Analysis Asymptotic methods Asst #2 Due Sophie Introduction to Prob. Mariolys Limit Laws and Comb Marni And18 IX.1 the characteristic polynomial, det(λI − A) = 11 20 IX.2 23 IX.3 25 IX.4 13 30 IX.5 14 Dec 10 Random Structures and Limit Laws FS: Part C (rotating presentations) 12 Discrete Limit Laws Sophie Combinatorial instances of discrete Mariolys Continuous Limit Laws Marni Quasi-Powers and Gaussian limit laws Sophie Presentations Asst #3 Due 23 3 −6 Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY For example, if A = Version of: 11-Dec-09 det(A) = tr(A) = det(λI − A) = C EDRIC C HAUVE , FALL 2013 17 f a cu lty of science d epa r tm ent of m athema tic s Week Date Sections Part/ References MATH 895-4 Fall 2010 Course Schedule Topic/Sections MATH 232 S ECTION #4.4 Notes/Speaker from Theorem FS2009 (4.4.9) If A is a 2 × 2 matrix, then the characteristic polynomial 1 Sept 7 I.1, I.2, I.3 Symbolic methods of A14is I.4, I.5, I.6 Combinatorial Structures 2 Unlabelled structures 3 21 II.1, II.2, II.3 7 19 IV.3, IV.4 8 26 FS: Part A.1, A.2 Comtet74 Handout #1 (self study) Labelled structures I and 4 28 II.4, II.5, II.6 Labelled structures II (a) A has two distinct realCombinatorial eigenvalues if tr(A)2 − 4 det(A) Combinatorial 5 Oct 5 III.1, III.2 Asst #1 Due parameters Parameters (b) A has one repeated real eigenvalues if tr(A)2 − 4 det(A) FS A.III 6 12 IV.1, IV.2 Multivariable GFs (self-study) (c) A has two distinct conjugate complex eigenvalues if tr(A)2 − 4 det(A) Analytic Methods FS: Part B: IV, V, VI Appendix B4 Stanley 99: Ch. 6 Handout #1 (self-study) Complex Analysis Singularity Analysis IV.5 In Remark. V.1 fac...
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