01. Matrix Multiplication (4 ways)
02. Inverse Matrix
03. Gaussian - Jordan Method (find inverse matrix)
01. Matrix Multiplication (4 ways)
a. Element Way
01.png
b. Column Way
02.png
Columns of C is combination of columns of A.
c. Row Way
03.png
Rows of C is combination of rows of B
d. Matrix Overlay
04.png
e.Block Way
05.png
Divide A and B into blocks. Notice that the element of A and B is sub matrix and the counterpart of C is also sub matrix with corresponding shape. The element way still stands for matrix multiplication in blocks.
02. Inverse Matrix
a. Definition
The inverse matrix of squared matrix A is a matrix that has property below.
06.png
b.Singular
For a matrix A, if there exists a non zero vector s.t. Ax = 0, then A is singular and has no inverse matrix.
singular_proof.png
03. Gaussian - Jordan Method (find inverse matrix)
Gaussian_Jordan.png
