PDF-LinearAlgebra Determinants InversesRank D Appendix D LINEAR ALGEBRA DETERMINANTS INVERSES

1 Introduction D3 D2 Determinants D3 D21 Some Properties of Determinants D3 D22 Cramers Rule D5 D23 Homogeneous Systems D6 D3 Singular Matrices Rank D6 D31 Rank De64257ciency D7 D32 Rank of Matrix Sums and Products D7 D33 Singular Systems Partic. 1 Motivation A3 A2 Vectors A3 A21 Notational Conventions A4 A22 Visualization A5 A23 Special Vectors A5 A3 Vector Operations A5 A31 Transposition A6 A32 Equality A6 A33 Addition and Subtraction Calculus Functions of single variable Limit con tinuity and differentiability Mean value theorems Evaluation of definite and improper integrals Partial derivatives Total derivative Maxima and minima Gradient Divergence and Curl Vector identities Di Calculus Mean value theorems Theorems of integral calculus Evaluation of definite and improper integrals Partial Derivatives Maxima and mini ma Multiple integrals Fourier series Vector identities Directional derivatives Line Surface and Volume integ Hermitian skewHermitian and unitary matriceseigenvalues and eigenvectors diagonalisation of matrices CayleyHamilton Theorem Calculus Functions of single variable limit continuity and differentiability Mean value theorems Indeterminate forms and LHos brPage 1br Appendix A In Room Storage Appendix B Vacation Stay Appendix C Luggage Sto rage brPage 2br QV57347RI57347WKH57347RXVLQJ57347JUHHPHQW5735957347DSSOLFDWLRQ We know how to graph the inverse of a function, but now we will look into expressing a new inverse function. Like before, let’s keep in mind the “switching x and y” theory. f. -1. (x). The inverse of the function f(x), f. Functions. Composite Functions . (f. ◦. g)(x)=f(g(x)). Inverses and 1-to-1 Functions. Finding Formulas for Inverses. Graphing Functions and Their Inverses. Inverse Functions and Composition. All Lectures. David Woodruff. IBM Almaden. Massive data sets. Examples. Internet traffic logs. Financial data. etc.. Algorithms. Want nearly linear time or less . Usually at the cost of a randomized approximation. Alexander G. Ororbia II. The Pennsylvania State University. IST 597: Foundations of Deep Learning. About this chapter. Not a comprehensive survey of all of linear algebra. Focused on the subset most relevant to deep learning. 1. Chapter Content. Determinants by Cofactor Expansion. Evaluating Determinants by Row Reduction. Properties of the Determinant Function. A Combinatorial Approach to Determinants. 2014/1/19. Elementary Linear Algebra. Proof.V=V1


Vq;AV=AV1


AVqA=C1


Cn;Vj=264v1...vn375AVj=C1


Cn264v1...vn375=v1C1+v2C2+


vnCn2colAcol(AV)=spanfAV1;
& Thm.[B] LetX1;X2;


;Xkbeeigenvectorscorrespondingto distinct eigenvalues1;2;


;kofA.ThenfX1;X2;


;Xkgis linearlyindependent . Proof.AssumethatfX1;X2;
&# and . Vector Calculus . and . Calculus of several Variables. Details of the Course M - 107. Math - 107 . Vectors and Matrices (3+0) credit-hours.. 1438– 1439 . H. 2. Dr.Khawaja. Zafar . Elahi. Xin Qian. BNL. 1. Introduction. Linear Algebra (LA) has a very long history:. First appears in “The Nine Chapters on the Mathematical Art” . Systematically i. ntroduced by Rene Descartes. Application of LA is very broad:.