======Notes on Gilbert Strang Linear Algebra======

Course 18.065 at MIT

https://ocw.mit.edu/courses/mathematics/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/syllabus/18.065-course-introduction/

Youtube Playlist of 35 lectures via MIT OpenCourseWare

Four topics:

1. The Column space of A contains all vectors Ax

A is matrix, x is vector

Multiply a matrix by a vector

Ax

dot product

column space C

row space R

independent columns

rank = the number of independent columns

a rank 1 matrix gives a line - the domain of "linear" algebra

a rank 2 matrix gives a plane, the column space is a plane, two independent columns one dependent column.  the two independent columns is the //basis// of the column space

A = C R

column rank == row rank

C transpose = R

C(A<sup>T</sup>) == row space