Python解决线性代数问题之矩阵的初等变换方法
定义一个矩阵初等行变换的类
class rowTransformation(): array = ([[],[]]) def __init__(self,array): self.array = array def __mul__(self, other): pass # 交换矩阵的两行 def exchange_two_lines(self,x,y): a = self.array[x-1:x].copy() self.array[x-1:x] = self.array[y-1:y] self.array[y-1:y] = a return self.array # 以k不等于0乘以矩阵中的某x行 def multiply(k,x,self): self.array[x-1:x] = k*self.array[x-1:x] return self.array # 把x行所有元的k倍加到另y行上去 def k_mul_arr_add_arr(self,k,x,y): self.array[y-1:y] += k*self.array[x-1:x] return self.array
定义一个初等列变换的类
# 封装一个初等列变换类 class colTransformation(): array = ([[],[]]) def __init__(self, array): self.array = array def __mul__(self, other): pass # 交换矩阵的两列 def exchange_two_lines(self, x, y): a = self.array[:, x-1:x].copy() self.array[:, x-1:x] = self.array[:, y-1:y] self.array[:, y-1:y] = a return self.array # 以k不等于0乘以矩阵中的某x列 def multiply(self, k, x): self.array[:, x-1:x] = k*self.array[:, x-1:x] return self.array # 把x列所有元的k倍加到另y列上去 def k_mul_arr_add_arr(self, k, x, y): self.array[:, y-1:y] += k*self.array[:, x-1:x] return self.array
求矩阵的秩
b = np.array([[2,-1,-1,1,2],[1,1,-2,1,4],[4,-6,2,-2,4],[3,6,-9,7,9]]) a = np.linalg.matrix_rank(b) print(a) 3
求非齐次线性方程组的解
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