Metric

• If the matrix has m rows and n columns, we say the size of the matrix is m by n,writen m * n
• We use $M_mxn$ to denote the set that contains all matrices whose size is m * n $\begin{bmatrix} 1 &2 \\2 &3 \\3 & 2 \end{bmatrix} \in M_{3*2}$

Ps:先 rows 再 columns

Index of component

the scalas in the i-th row and j-th column is called (i,j)-entry in the matrix

$A = \begin{bmatrix} a_{11}&a_{12}&...&a_{1n} \\a_{21}&a_{22}&...&a_{2n} \\ ...&...&...&...\\ a_{n1}&a_{n2}&...&a_{nn} \end{bmatrix}$

also:

$A = \begin{bmatrix} a_1 & a_2 & ... & a_n \end{bmatrix} : a_x$ is a vector

• Two matrices with the same size can add or substract
• Matrix can multiply by a scalar

Properties

A、B、C are m*n matrices,and s and t are scalars

• A + B = B + A
• (A + B) + C = A + (B + C)
• (st)A = s(tA)
• s(A + B) = sA + sB
• (s + t)A = sA + tA