PPT-ECE 417 Lecture 5: Eigenvectors

Mark HasegawaJohnson 9122017 Content Linear transforms Eigenvectors Eigenvalues Symmetric matrices Symmetric positive definite matrices Covariance matrices Principal components Linear Transforms. 1 Fig 92 brPage 6br Version 2 ECE IIT Kharagpur cos cos Fig93pgm k 12 otherwise truncated is if brPage 7br Version 2 ECE IIT Kharagpur 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Non-Commuting). . Random Symmetric Matrices? :. . A "Quantum Information" Inspired Answer. . Alan Edelman. Ramis. . Movassagh. July 14, 2011. FOCM. Random Matrices. Example Result. p=1 .  classical probability. . can. be . interpreted. as a file of data. A . matrix. . is. a . collection. of . vectors. and . can. be . interpreted. as a data . base. The. red . matrix. . contain. . three. . column. D. EFORMATION. . OF. 3. D. M. ODELS. Tamal. K. . Dey. , . Pawas. . Ranjan. , . Yusu. Wang. [The Ohio State University]. (CGI 2012). Problem. Perform deformations without asking the user for extra structures (like cages, skeletons . Hung-yi Lee. Chapter 5. In chapter 4, we already know how to consider a function from different aspects (coordinate system). Learn how to find a “good” coordinate system for a function. Scope. : Chapter 5.1 – 5.4. and . eigenvectors. Births. Deaths. Population. . increase. Population. . increase. = . Births. – . deaths. t. Equilibrium. N: . population. . size. b: . birthrate. d: . deathrate. The. net . Spring 2011. Dmitri Strukov. Partially adapted from Computer Organization and Design, 4. th. edition, Patterson and Hennessy,. Agenda. Instruction formats. Addressing modes. Advanced concepts. ECE 15B Spring 2011. Prepared by Vince Zaccone. For Campus Learning Assistance Services at UCSB. Prepared by Vince Zaccone. For Campus Learning Assistance Services at UCSB. Consider the equation . , where A is an . nxn. Prepared by Vince Zaccone. For Campus Learning Assistance Services at UCSB. Prepared by Vince Zaccone. For Campus Learning Assistance Services at UCSB. Consider the equation . , where A is an . nxn. Case I: real eigenvalues of multiplicity 1. MAT 275. Let . and . be two functions. A system of differential equations can have the form. where . and . are constants. This is an example of a linear system of ODEs with constant coefficients.. Chap 3 -. 1. . ECE 271. Electronic Circuits I. Topic 3. Diodes and Diodes Circuits. NJIT ECE-271 Dr. S. Levkov. Chapter Goals. Develop electrostatics of the . pn. junction. Define regions of operation of the diode (forward bias, reverse bias, and reverse breakdown). Topic 8. - . 1. Topic 8. . Complementary MOS (CMOS) Logic Design. ECE 271. Electronic Circuits I. NJIT ECE 271 Dr, Serhiy Levkov. Topic 8. - . 2. Chapter Goals. Introduce CMOS logic concepts. Explore the voltage transfer characteristics of CMOS inverters. Review. If . . (. is a vector, . is a scalar). . is an eigenvector of A . . is an eigenvalue of A that corresponds to . . Eigenvectors corresponding to . are . nonzero. solution . of . (. A. . .,2('5 WXL7!)7!#$%#&'#+!8;'!)-74!,1&.#)7#+!%)',#1'7K!&()1&#!4�!+/,125Q!A(#!�,1+,12!0)7!+#3)7')',125!='!&()12#+!14'!41-/!(40!0#!'.#)'!(#).' A(#.#!,7!)!-412!-,7'!4�!*#+,&)-!%.4&#+;.