Skip to content

Commit

Permalink
Update linearAgrbra.md
Browse files Browse the repository at this point in the history
  • Loading branch information
870138612 authored Oct 31, 2024
1 parent 96fb528 commit cdd4a78
Showing 1 changed file with 3 additions and 22 deletions.
25 changes: 3 additions & 22 deletions src/note/linearAgrbra.md
Original file line number Diff line number Diff line change
Expand Up @@ -304,25 +304,6 @@ $$
$$
矩阵乘法不满足交换律.

$$
(A+B)^2=(A+B)(A+B)=A^2+AB+BA+B^2 \not = A^2+2AB+B^2,
$$
$$
(A-B)^2=(A-B)(A-B)=A^2-AB-BA+B^2 \not = A^2-2AB+B^2,
$$
$$
(A+B)(A-B)=A^2+BA-AB-B^2\not = A^2-B^2,
$$
$$
(AB)^m=(AB)(AB)\cdots (AB)\not = A^mB^m.
$$
若$f(x)=a_0+a_1x+\cdots+a_mx^m$,则

$$
f(A)=a_0E+a_1A+\cdots +a_mA^m.
$$

- 转置矩阵,将矩阵$A$行列互换得到的矩阵称为转置矩阵,记$A^T$.

Expand Down Expand Up @@ -357,11 +338,11 @@ $$

- 几种重要矩阵

- 单位矩阵:主对角线元素均为$1$,其余全为$0$的方阵称为单位矩阵,记$E$,单位矩阵能与任何同阶矩阵进行交换.
单位矩阵:主对角线元素均为$1$,其余全为$0$的方阵称为单位矩阵,记$E$,单位矩阵能与任何同阶矩阵进行交换.

- 对称矩阵:$A^T=A$.
对称矩阵:$A^T=A$.

- 反对称矩阵:$A^T=-A\Leftrightarrow\begin{cases}a_{ij}=-a_{ji},i\not= j\\a_{ii}=0. \end{cases}$
反对称矩阵:$A^T=-A\Leftrightarrow\begin{cases}a_{ij}=-a_{ji},i\not= j\\a_{ii}=0. \end{cases}$

- 分块矩阵的运算
$$
Expand Down

0 comments on commit cdd4a78

Please sign in to comment.