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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