Lecture 13: Randomized Matrix Multiplication

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Description This lecture focuses on randomized linear algebra, specifically on randomized matrix multiplication. This process is useful when working with very large matrices. Professor Strang introduces and describes the basic steps of randomized computations. Summary Sample a few columns of \(A\) and rows of \(B\) Use probabilities proportional to lengths \(\Vert A_i \Vert \, \Vert B_i \Vert\) See the key ideas of probability: Mean and Variance Mean \(= AB\) (correct) and variance to be minimized Related section in textbook: II.4 Instructor: Prof. Gilbert Strang