Lecture 5 - Background on Linear Algebra and Probability Theory

Lecture 5 - Background on Linear Algebra and Probability Theory

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PATTERN RECOGNITION Professor Aly A. Farag Computer Vision and Image Processing Laboratory University of Louisville URL: www.cvip.uofl.edu ; E-mail: aly.farag@louisville.edu ________________________________________________________________________ Planned for ECE 620 and ECE 655 - Summer 2011 TA/Grader: Melih Aslan; CVIP Lab Rm 6, msaslan01@lousiville.edu Lecture 5: Background on Linear Algebra and Probability Theory
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Linear Algebra
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Linear algebra Matrix A: Matrix Transpose Vector a mn m m n n n m ij a a a a a a a a a a A ... ... ... ... ... ... ... ] [ 2 1 2 22 21 1 12 11 m j n i a b A b B ji ij T m n ij 1 , 1 ; ] [ ] ,..., [ ; ... 1 1 n T n a a a a a a
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Matrix and vector multiplication Matrix multiplication Outer vector product Vector-matrix product ) ( ) ( , ] [ ; ] [ ; ] [ B col A row c where c C AB b B a A j i ij n m ij n p ij p m ij matrix n m an AB b a c b B b a A a n ij T m ij , ; ] [ ; ] [ 1 1 m length of vector matrix m an Ab C b B b a A n ij n m ij 1 ; ] [ ; ] [ 1
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Inner Product Inner (dot) product: Length (Eucledian norm) of a vector a is normalized iff ||a|| = 1
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Lecture 5 - Background on Linear Algebra and Probability Theory

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