Normed vector space: definition and examples of vector and matrix norms

Definition of a norm, normed linear vector space and examples (L1,L2,Lp,L0,L1/2), norm as a distance function, metric space, applications of vector norms

00:45 recap on a vector space
04:15 definition of a norm
07:16 examples of vector and matrix norms (L1,L2,Linf)
13:34 Lp-norm, L0, and L1/2, unit-norm balls
18:30 L0-norm is NOT truly a norm
19:58 L1/2-norm is NOT truly a norm
22:06 norm a distance function (taxicab, Euclidean, Minkowski, Chebyshev)
26:00 distance of a point to a set
31:35 metric space, distance function
34:40 distance between a point and a set, distance between two sets
39:35 applications of vector norms

Instructor: Jitkomut Songsiri, Chulalongkorn University, Thailand