Lecture 16: Derivatives of Inverse and Singular Values

Description

In this lecture, Professor Strang reviews how to find the derivatives of inverse and singular values. Later in the lecture, he discusses LASSO optimization, the nuclear norm, matrix completion, and compressed sensing.

Summary

Derivative of \(A^2\) is \(A(dA/dt)+(dA/dt)A\): NOT \(2A(dA/dt)\).
The inverse of \(A\) has derivative \(-A^{-1}(dA/dt)A^{-1}\).
Derivative of singular values \(= u(dA/dt)v^{\mathtt{T}} \)
Interlacing of eigenvalues / Weyl inequalities

Related section in textbook: III.1-2

Instructor: Prof. Gilbert Strang