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HomeMIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018Lecture 15: Matrices A(t) Depending on t, Derivative = dA/dt
Lecture 15: Matrices A(t) Depending on t, Derivative = dA/dt
50:52
Description
This lecture is about changes in eigenvalues and changes in singular values. When matrices move, their inverses, their eigenvalues, and their singular values change. Professor Strang explores the resulting formulas.
SummaryMatrices \(A(t)\) depending on \(t / \)Derivative \(= dA/dt\)
The eigenvalues have derivative \(y(dA/dt)x\).\(x\) = eigenvector, \(y\) = eigenvector of transpose of \(A\)
Eigenvalues from adding rank-one matrix are interlaced.
Related section in textbook: III.1-2
Instructor: Prof. Gilbert Strang
