PPT-Rank Bounds for Design Matrices and Applications

Shubhangi Saraf Rutgers University Based on joint works with Albert Ai Zeev Dvir Avi Wigderson Sylvester Gallai Theorem 1893 v v v v Suppose that every line through . It is essential that you do some reading but the topics discussed in this chapter are adequately covered in so many texts on linear algebra that it would be arti64257cial and unnecessarily limiting to specify precise passages from precise texts The 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 Shubhangi. . Saraf. Rutgers University. Based on joint works with . Albert Ai, . Zeev. . Dvir. , . Avi. . Wigderson. Sylvester-. Gallai. Theorem (1893). v. v. v. v. Suppose that every line through . fanin. Neeraj Kayal. Chandan. . Saha. Indian Institute of Science. A lower bound. Theorem: . Consider representations of a degree d polynomial . . of the form . If the . ’s . have . degree one and . Aswin C Sankaranarayanan. Rice University. Richard G. . Baraniuk. Andrew E. Waters. Background subtraction in surveillance videos. s. tatic camera with foreground objects. r. ank 1 . background. s. parse. Load balancing (computing). Load balancing is a computer networking method for distributing workloads across multiple computing resources, such as computers, a computer cluster, network links, central processing units or disk drives. Load balancing aims to optimize resource use, maximize throughput, minimize response time, and avoid overload of any one of the resources. . IT530 Lecture Notes. Matrix Completion in Practice: Scenario 1. Consider a survey of M people where each is asked Q questions. . It may not be possible to ask each person all Q questions.. Consider a matrix of size M by Q (each row is the set of questions asked to any given person).. Matrix Algebra and the ANOVA. Matrix properties. Types of matrices. Matrix operations. Matrix algebra in Excel. Regression using matrices. ANOVA in matrix notation. Definition of a . Matrix. a . matrix. Matrices. Definition: A matrix is a rectangular array of numbers or symbolic elements. In many applications, the rows of a matrix will represent individuals cases (people, items, plants, animals,...) and columns will represent attributes or characteristics. Lectures 1-2. 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. 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. Niebles. . and Ranjay Krishna. Stanford Vision and Learning . Lab. 10/2/17. 1. Another, very in-depth linear algebra review from CS229 is available here:. http://cs229.stanford.edu/section/cs229-linalg.pdf. What is a matrix?. A Matrix is just rectangular arrays of items. A typical . matrix . is . a rectangular array of numbers arranged in rows and columns.. Sizing a matrix. By convention matrices are “sized” using the number of rows (m) by number of columns (n).. This Slideshow was developed to accompany the textbook. Precalculus. By Richard Wright. https://www.andrews.edu/~rwright/Precalculus-RLW/Text/TOC.html. Some examples and diagrams are taken from the textbook..