DS_Lecture_12.pdf - Lecture 12 Matrices Dr Chengjiang Long Computer Vision Researcher at Kitware Inc Adjunct Professor at SUNY at Albany Email

# DS_Lecture_12.pdf - Lecture 12 Matrices Dr Chengjiang Long...

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Lecture 12: Matrices Dr. Chengjiang Long Computer Vision Researcher at Kitware Inc. Adjunct Professor at SUNY at Albany. Email: [email protected]

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C. Long Lecture 12 September 28, 2018 2 ICEN/ICSI210 Discrete Structures Important timeline Midterm exam 1 Midterm exam 2 Final exam Midterm exam 1: Oct 8th, 2018 (Monday) at LC-25, 9:20am – 11:20am. Coverage : Chap 1.1 -1.8, 2.1-2.6, Lecture slides 2-12. Format : 5 Problems and the 1 st one is True/False Problem. The rest problems are in the similar format of homework sets. Exam policy : close book, close note. Important Propositional Equivalences will be given if necessary. Extra points are available now!
C. Long Lecture 12 September 28, 2018 3 ICEN/ICSI210 Discrete Structures Outline Introduction to Matrix Matrix Arithmetic Zero-One Matrices

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C. Long Lecture 12 September 28, 2018 4 ICEN/ICSI210 Discrete Structures Outline Introduction to Matrix Matrix Arithmetic Zero-One Matrices
C. Long Lecture 12 September 28, 2018 5 ICEN/ICSI210 Discrete Structures Introduction •Scalars: A single number •Vector: A 1D array of numbers, where each element is identified by an single index •Matrix: A 2D array of numbers

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C. Long Lecture 12 September 28, 2018 6 ICEN/ICSI210 Discrete Structures Matrix Matrices are useful discrete structures that can be used in many ways. For example, they are used to: describe certain types of functions known as linear transformations. Express which vertices of a graph are connected by edges.
C. Long Lecture 12 September 28, 2018 7 ICEN/ICSI210 Discrete Structures Linear transformation

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C. Long Lecture 12 September 28, 2018 8 ICEN/ICSI210 Discrete Structures Matrix: a graph are connected by edges
C. Long Lecture 12 September 28, 2018 9 ICEN/ICSI210 Discrete Structures Matrix Definition : A matrix is a rectangular array of numbers. A matrix with m rows and n columns is called an m × n matrix. The plural of matrix is matrices . A matrix with the same number of rows as columns is called square . Two matrices are equal if they have the same number of rows and the same number of columns and the corresponding entries in every position are equal. 3 2 matrix 3 by 2 matrix

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C. Long Lecture 12 September 28, 2018 10 ICEN/ICSI210 Discrete Structures Notation Let m and n be positive integers and let The i- th row of A is the n matrix [ a i 1 , a i 2 ,…,a in ]. The j- th column of A is the m ×1 matrix: The ( i,j )-th element or entry of A is the element a ij . We can use A = [ a ij ] to denote the matrix with its ( i,j )-th element equal to a ij .
C. Long Lecture 12 September 28, 2018 11 ICEN/ICSI210 Discrete Structures Types of Matrices

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