有名有姓的Matrix

Square Matrix

m = n 方形矩阵拥有对角线 diagonal

Upper Triangular Matrix

左下角为0

$\begin{bmatrix} 2&3&5\\0&3&5\\0&0&3 \end{bmatrix}$

Lower Triangulare Matrix

右上角为0

$\begin{bmatrix} 2&0&0\\1&3&0\\3&2&3 \end{bmatrix}$

Diagonal Matrix

All non-diagonal elements are "0"

$\begin{bmatrix} 2&0&0\\0&3&0\\0&0&3 \end{bmatrix}$

Identity Matrix

Denoted by $I$(any size ), or $I_n$ ,很常用

$I_3 = \begin{bmatrix} 1&0&0\\0&1&0\\0&0&1 \end{bmatrix}$

Zero Matrix

Denoted by O (any size), or $O_m*n$

$O = \begin{bmatrix} 0&0&0\\0&0&0 \end{bmatrix}$

Transpose

If $A$ is an mn matrix,$A^T$ (transpose of $A$) is an nm matrix whose (i,j)-entry is (j,i)-entry of $A^T$

Properties

• $A$ and $B$ are m*n matrices,and s is scalar
• $(A^T)^T = A$
• $(sA)^T = sA^T$
• $(A+B)^T = A^T + B^T$

Symmetric Matrix

$A^T=A$