Lecture 15: Matrices A(t) Depending on t, Derivative = dA/dt

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.

Summary

Matrices \(A(t)\) 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