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Update chapter03.ipynb #23

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2 changes: 1 addition & 1 deletion chapter03.ipynb
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Expand Up @@ -48,7 +48,7 @@
"\n",
"观察这个方阵，我们如果用另一个矩阵乘$A$，则得到的结果矩阵中的每一列应该都是$\\begin{bmatrix}1\\\\2\\end{bmatrix}$的倍数，所以我们不可能从$AB$的乘积中得到单位矩阵$I$。\n",
"\n",
"另一种判定方法，如果$A$乘以任意非零向量能够得到$0$向量，则矩阵$A$不可逆，即使用$Ax=0$判定。我们来用上面的矩阵为例：$\\begin{bmatrix}1&2\\\\3&6\\end{bmatrix}\\begin{bmatrix}3\\\\-1\\end{bmatrix}=\\begin{bmatrix}0\\\\0\\end{bmatrix}$。\n",
"另一种判定方法，如果$A$乘以任意非零向量能够得到$0$向量，则矩阵$A$不可逆，即使用$Ax=0$判定。我们来用上面的矩阵为例：$\\begin{bmatrix}1&3\\\\2&6\\end{bmatrix}\\begin{bmatrix}3\\\\-1\\end{bmatrix}=\\begin{bmatrix}0\\\\0\\end{bmatrix}$。\n",
"\n",
"证明：如果对于非零的$x$仍有$Ax=0$，而$A$有逆$A^{-1}$，则$A^{-1}Ax=0$，即$x=0$，与题设矛盾，得证。\n",
"\n",
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