Lecture 8: Norms of Vectors and Matrices

Description

A norm is a way to measure the size of a vector, a matrix, a tensor, or a function. Professor Strang reviews a variety of norms that are important to understand including S-norms, the nuclear norm, and the Frobenius norm.

Summary

The \(\ell^1\) and \(\ell^2\) and \(\ell^\infty\) norms of vectors
The unit ball of vectors with norm \(\leq\) 1
Matrix norm = largest growth factor = max \( \Vert Ax \Vert / \Vert x \Vert\)
Orthogonal matrices have \(\Vert Q \Vert_2 = 1\) and \(\Vert Q \Vert^2_F = n\)

Related section in textbook: I.11

Instructor: Prof. Gilbert Strang