线性代数Python计算：矩阵的线性运算

Posted 2022-06-15 戌崂石

给定正整数$m$和$n$和数域$P$，
$\forall \mathbf{A}=\left(\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& ⋮& \cdots & ⋮\\ a_{m1}& a_{m2}& \cdots & a_{mn}\end{array}\right),\mathbf{B}=\left(\begin{array}{cccc}{b}_{11}& b_{12}& \cdots & b_{1n}\\ b_{21}& b_{22}& \cdots & b_{2n}\\ ⋮& ⋮& \cdots & ⋮\\ b_{m1}& b_{m2}& \cdots & b_{mn}\end{array}\right)\in P^{m\times n}$，定义$\mathbf{A}$与$\mathbf{B}$的和为：
$$\mathbf{C}=\mathbf{A}+\mathbf{B}=\left(\begin{array}{cccc}{a}_{11}+b_{11}& a_{12}+b_{12}& \cdots & a_{1n}+b_{1n}\\ a_{21}+b_{21}& a_{22}+b_{23}& \cdots & a_{2n}+b_{2n}\\ ⋮& ⋮& \cdots & ⋮\\ a_{m1}+b_{m1}& a_{m2}+b_{m2}& \cdots & a_{mn}+b_{mn}\end{array}\right)\in P^{m\times n}.$$
定义$\lambda$与$\mathbf{A}$的积：
λ ⋅ A = ( λ a 11 λ a 12 ⋯ λ a 1 n λ a 21