#範例14-3：求矩陣核空間的基底
#（1）sympy求解
from sympy import *
M = Matrix([
    [1,3,-2,0,2,0],
    [2,6,-5,-2,4,-3],
    [0,0,5,10,0,15],
    [2,6,0,8,4,18]
    ])
M_simple = M.rref()
print('顯示高斯消去法簡化的梯形矩陣的echelon form =\n', M_simple)
M_rank = M.rank()
M_dim = M.shape[1]
M_nullity = M_dim - M_rank

print('輸入空間維度 = input dimension of M=', M_dim)
print('輸出空間維度 = rank(M)=', M_rank)
print('核空間維度 = 被轉換壓縮的空間維度 = nullity=', M_nullity)
M_nullsapce = M.nullspace()
M_columnspace = M.columnspace()
print('線性轉換後有壓縮空間 = 核空間向量集合 = null space=\n', M_nullsapce)
print('輸出行空間的向量之線性組和= column space= \n', M_columnspace)