概念
零矩阵<span class="equation-text" contenteditable="false" data-index="0" data-equation="O"><span></span><span></span></span>：元素都是0
同型矩阵：两个矩阵行列数相等，则称它们俩是同型矩阵
n阶方阵A的行列式：由方阵A的所有元素构成的行列式
运算
加法：两矩阵行列数相等才能进行相加
数乘：一个数k乘一个矩阵A，得到的矩阵为A的每个元素都乘k
乘法：当A的列数=B的行数时，可以进行AB的运算<br>新矩阵里元素ij等于A的第i行乘B的第j列
注意：<br>1.一般情况下无交换律，即<span class="equation-text" data-index="0" data-equation="AB\not=BA" contenteditable="false"><span></span><span></span></span><br>2.无消去律，即<span class="equation-text" data-index="1" data-equation="AB=AC\nRightarrow B=C" contenteditable="false"><span></span><span></span></span><br>3.当<span class="equation-text" data-index="2" data-equation="A\not=O,B\not=O" contenteditable="false"><span></span><span></span></span>时，有可能<span class="equation-text" data-index="3" data-equation="AB=O" contenteditable="false"><span></span><span></span></span><br> 或者说当<span class="equation-text" data-index="4" data-equation="AB=O" contenteditable="false"><span></span><span></span></span>时<span class="equation-text" data-index="5" data-equation="\nRightarrow A=O" contenteditable="false"><span></span><span></span></span>或<span class="equation-text" contenteditable="false" data-index="6" data-equation="B=O"><span></span><span></span></span>
单位矩阵<span class="equation-text" contenteditable="false" data-index="0" data-equation="E"><span></span><span></span></span>
对角矩阵<span class="equation-text" contenteditable="false" data-index="0" data-equation="\Lambda"><span></span><span></span></span>
<span class="equation-text" data-index="0" data-equation="\Lambda_1\Lambda_2=\Lambda_2\Lambda_1" contenteditable="false"><span></span><span></span></span>
<span class="equation-text" data-index="0" data-equation="\Lambda^n=主对角线元素n次方" contenteditable="false"><span></span><span></span></span>
<span class="equation-text" data-index="0" data-equation="\Lambda^{-1}=主对角线元素都取倒数" contenteditable="false"><span></span><span></span></span>
当<span class="equation-text" data-index="0" data-equation="\alpha,\beta" contenteditable="false"><span></span><span></span></span>都是n维列向量时，看到<span class="equation-text" contenteditable="false" data-index="1" data-equation="\alpha\beta^T,\alpha^T\beta,\beta\alpha^T,\beta^T\alpha"><span></span><span></span></span>，要注意观察哪些是数，哪些是矩阵
转置矩阵
<span class="equation-text" contenteditable="false" data-index="0" data-equation="(A+B)^T=A^T+B^T"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="(kA)^T=kA^T"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="(AB)^T=B^TA^T"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="(A^T)^T=A"><span></span><span></span></span>
