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<meta property="og:description" content="第九讲：线性相关性、基、维数 线性相关性 背景知识:假设一个矩阵A，m&lt;n，即未知数个数大于方程数，因此在零空间内除了零向量之外还有别的向量，最多m个主元，存在n-m个自由向量，整个方程存在非零解。 什么条件下，\(x_1,x_2,x_3...x_n\)线性无关?存在一个系数不全为零的组合，使得线性相加结果为0,则为线性相关，反之为线性无关。 如果向量组里存在一个零向量，则这个向量组不可">
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15 changes: 10 additions & 5 deletions 2017/01/22/LinearAlgebra3/index.html
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<meta property="og:description" content="第十七讲：行列式及其性质 行列式 矩阵A的行列式是与矩阵相关的一个数，记作\(detA或者|A|\) 行列式的性质 \(detI&#x3D;1\) 交换行，行列式的值的符号会相反 一个置换矩阵的行列式是1或-1，取决于交换行次数的奇偶 两行相等使得行列式为0(由性质二可以直接推出) 矩阵消元不改变其行列式(证明见下) 某一行为0，行列式为0(与0相乘等价于某一行为0，结果为0) \(detA&#x3D;0\)当且">
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