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Matrix Calculus 2020 04 16 for MIT Linear Algebra 18.06 Spring 2020 (Alan Edelman)

The Julia Programming Language
87.8K subscribers
17K views 4 years ago
This video posted after reading this tweet: https://twitter.com/AlanEdelmanMIT/st... For more info, follow us on Twitter at   / julialanguage   Contents 00:00 Matrix calculus 01:28 Scalar calculus 09:03 Emphasis on linearization 14:23 Gradients 17:23 Geometrically 24:16 Matrix/vector product rule 29:57 Gradients the straightforward but klunky way 30:41 Gradients the sophisticated way 33:42 Example f(x) = (Ax - b)'(Ax - b) 37:41 Gradient notation 38:28 The trace 42:50 Linear functions of matrices 46:20 Gradients of functions from matrices to scalars 51:20 Vector to vector Jacobians 54:59 How are gradients used 55:48 The Jacobian matrix, vectors to vectors 1:05:55 A key point: you don't have to write out the matrix elements 1:06:27 Relationship to volumes 1:07:55 Matrices to matrices 1:08:48 Derivatives of matrix to matrix functions Want to help add timestamps to our YouTube videos to help with discoverability? Find out more here: https://github.com/JuliaCommunity/You... Interested in improving the auto generated captions? Get involved here: https://github.com/JuliaCommunity/You... ...more
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Matrix calculus

0:00

Scalar calculus

1:28

Emphasis on linearization

9:03

Gradients

14:23

Geometrically

17:23

Matrix/vector product rule

24:16

Gradients the straightforward but klunky way

29:57

Gradients the sophisticated way

30:41

Example f(x) = (Ax - b)'(Ax - b)

33:42

Gradient notation

37:41

The trace

38:28

Linear functions of matrices

42:50

Gradients of functions from matrices to scalars

46:20

Vector to vector Jacobians

51:20

How are gradients used

54:59

The Jacobian matrix, vectors to vectors

55:48

A key point: you don't have to write out the matrix elements

1:05:55

Relationship to volumes

1:06:27

Matrices to matrices

1:07:55

Derivatives of matrix to matrix functions

1:08:48
Matrix Calculus 2020 04 16 for MIT Linear Algebra 18.06 Spring 2020 (Alan Edelman)
511Likes
17,881Views
2020Dec 22
This video posted after reading this tweet: https://twitter.com/AlanEdelmanMIT/st... For more info, follow us on Twitter at   / julialanguage   Contents 00:00 Matrix calculus 01:28 Scalar calculus 09:03 Emphasis on linearization 14:23 Gradients 17:23 Geometrically 24:16 Matrix/vector product rule 29:57 Gradients the straightforward but klunky way 30:41 Gradients the sophisticated way 33:42 Example f(x) = (Ax - b)'(Ax - b) 37:41 Gradient notation 38:28 The trace 42:50 Linear functions of matrices 46:20 Gradients of functions from matrices to scalars 51:20 Vector to vector Jacobians 54:59 How are gradients used 55:48 The Jacobian matrix, vectors to vectors 1:05:55 A key point: you don't have to write out the matrix elements 1:06:27 Relationship to volumes 1:07:55 Matrices to matrices 1:08:48 Derivatives of matrix to matrix functions Want to help add timestamps to our YouTube videos to help with discoverability? Find out more here: https://github.com/JuliaCommunity/You... Interested in improving the auto generated captions? Get involved here: https://github.com/JuliaCommunity/You...

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The Julia Programming Language

87.8K subscribers