First to go over the basics of Matrix as is shown below
Second, Dr.Strang sure will go over the four fundamental subspaces of Matrix A that is mxn of rank r: the column space of A, column space of A transpose (row space of A), null space of A and null space of A transpose.
Use the below concrete example to understand the relationship of row space, column space of A, of A transpose, null space of A, of A transpose, and dimensions:
Next, reiterate how important “Positive Definite and Semidefinite Matrices” is. How to check if it is positive definite and semidefinite matrix?
What really reignite knowledge points is the second point: Energy xTSx >= 0 for all vector x not equal to zero vector. It is called Energy as is linked to the law in physics in describing energy!
On Dec 18th, 2022, enhancing understanding of matrix from Prof. Strang again on this series.
Naixian Zhang 