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MIT 18.065: Matrix Methods in Data Analysis, Signal Processing, and Machine Learning →0/14
1

Eckart-Young: The Closest Rank k Matrix to A

47:16
2

Norms of Vectors and Matrices

49:21
3

Four Ways to Solve Least Squares Problems

49:51
4

Survey of Difficulties with Ax = b

49:36
5

Minimizing "x" Subject to Ax = b

50:22
6

Computing Eigenvalues and Singular Values

49:28
7

Randomized Matrix Multiplication

52:24
8

Low Rank Changes in A and Its Inverse

50:34
9

Matrices A(t) Depending on t, Derivative = dA/dt

50:52
10

Derivatives of Inverse and Singular Values

43:08
11

Rapidly Decreasing Singular Values

50:34
12

Counting Parameters in SVD, LU, QR, Saddle Points

49:00
13

Saddle Points Continued, Maxmin Principle

52:13
14

Definitions and Inequalities

55:01

Matrices A(t) Depending on t, Derivative = dA/dt

Gilbert StrangDistinguishedMIT

Professor

50:52·2019·graduate level

This lecture examines how eigenvalues and singular values change when matrices evolve over time, deriving essential formulas for their derivatives.

MathematicsLinear AlgebraCalculus & AnalysisControl & Dynamical SystemsMatrix Calculus

MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018

Instructor: Gilbert Strang

View the complete course: https://ocw.mit.edu/18-065S18

YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k

LecturerAll lecturers →
Gilbert StrangDistinguished

MIT Professor Emeritus & Author of Introduction to Linear Algebra

MIT Professor of Mathematics Emeritus whose legendary 18.06 Linear Algebra and 18.085 Computational Science courses educated millions of engineers and mathematicians.

3 courses · 56 lecturesCanon
Previous · Lecture 8

Low Rank Changes in A and Its Inverse

Next · Lecture 10

Derivatives of Inverse and Singular Values

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