3.1 Matrices and vectors
Matrix: Rectangular array of numbers. (A B C)
Dimension of matrix : number of rows x number of columns
Matrix Elements (entires of matrix) :
Vector: An n x 1 matrix. (a, b, c)
1- indexed vs 0- indexed :
y=\left\lbrack\matrix{y_1\y_2\y_3\y_4}\right\rbrack vs y=\left\lbrack\matrix{y_0\y_1\y_2\y_3}\right\rbrack
又是一段CSDN显示不出来的公式…
we use 1- indexed
3.2 Addition and scalar multiplication(标量乘法)
3.3 Matrix-vector multiplication
House sizes : \matrix{2104 \ 1416\1532\852} \quad \quad h_{\theta}(x)=-40+0.25x
matrix : \left\lbrack\matrix{1 & 2104\1 & 1416\1&1532\1&852}\right\rbrack \times \left\lbrack\matrix{-40\0.25}\right\rbrack =
依旧显示不出来
3.4 Matrix-matrix multiplication
House sizes : \matrix{2104 \ 1416\1532\852}
matrix : \left\lbrack\matrix{1 & 2104\1 & 1416\1&1532\1&852}\right\rbrack \times \left\lbrack\matrix{-40&200&-150\0.25&0.1&0.4}\right\rbrack =
…
3.5 Matrix multiplication properties
Identity Matrix:
3.6 Inverse and transpose(逆和转置)
Matrices that don’t have an inverse are “singular” (奇异) or “degenerate” (退化)