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Lecture Slides for Matrix Calculus Winter 2022 Alan Edelman/Steven Johnson 11am-1pm MWF 1 ● Lectures: January 10,12,14,19,21,24,26,28 ● 11am-1pm virtual, short break around noon ● Two Homeworks: Released Wednesday due following Wednesday on canvas, 11:59pm due ● 3 Credits ● Linear Algebra such as 18.06 assumed Some demos and hw may use (no experience assumed, though most LinAlg classes at MIT use a little Julia already) 2 Where does matrix calculus fit in? ● MIT 18.01: Scalar or Single Variable Calculus ● MIT 18.02: Vector or Multivariable Calculus Perhaps an ideal world might go Scalar, Vector, Matrix, Higher Dimensional Arrays… (0 dimensional, 1 dimensional, 2 dimensional…) (e.g. size(scalar)=[], size(vector)=[n], size(matrix)=[m,n],...) (some programming language do not implement this fully) Why now? ● In the last decade or two, the role of linear algebra has taken on larger importance in lots of areas including Machine Learning, Statistics, Engineering, etc. ● Warning: googling Matrix Calculus may only give a small view of the full range of the mathematics that we 2 hope to cover example what is the derivative of X when X is a square matrix? Should it be 2X? (It’s not). -1 -2 What about X ? -X ? (Not quite). 3 Applications: Machine Learning buzzwords: parameter optimization stochastic gradient descent, autodiff, backpropagation © University of Tubingen. All rights reserved. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use. © Medium (medium.com). All rights reserved. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use. © Medium (medium.com). All rights reserved. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use. 4 © Stack Exchange Inc. All rights reserved. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use.
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