V9: Review of Linear Algebra in Error-Correcting Codes

An introduction to error-correcting codes (with Alfred Menezes).

Topics covered: vector spaces, linear combination of vectors, span, linear dependence, linear independence, basis, dimension, matrices, rank, row space, column space, row rank, column rank, elementary row operations, null space, rank-nullity theorem, invertible matrices, non-singular matrices.

Course web page (includes slides, exercises and solutions): https://cryptography101.ca/codes

Lecture playlist: https://www.youtube.com/playlist?list=PLA1qgQLL41STeC3RoWeEONqX48dMjdLVY

Other cryptography courses: https://cryptography101.ca

Slides
00:00 Introduction
00:19 Slide 188: Vector spaces
01:46 Slide 189: Linear independence
03:39 Slide 190: Bases and dimension
04:33 Slide 191: Matrices
05:44 Slide 192: Example
06:49 Slide 193: Rank of a matrix
07:33 Slide 194: Example (1)
09:14 Slide 195: Example (2)
10:12 Slide 196: Null space and invertibility