Teacher：Gilbert Strang

The text of the course: Introduction to Linear Algebra

Website:web.mit.edu/18.06,which got a lot of exercise from the past MATLAB codes, the syllabus for the course

Lecture 14

orthogonal subspace

row space is orthogonal to nullspace,
columnspace is orthongonal to nullspace of A^T.
Subspace S is orthogonal to subspace T
mean:every vector in S is orthogonal to every vector in T.
rowspace is orthogonal to nulspace. Why?
nullspace and rowspace are orthogonal complement in R⁴.
nullspace contains all vectors 垂直于 row space.

Coming: Ax=b when there is no solution, ------A^TAx’=A^Tb

“solve” the equations.
A^TA have these properties: (A^TA)^T=A^TA; n*n;
N(A^TA)=N(A); rank of A^TA=rank of A.
A^TA is invertible exactly if A has indep column.