#範例14-4:求矩陣核空間的基底 #(1)sympy求解 from sympy import * M = Matrix([ [1,-2,5,0,3], [0,1,3,0,0], [0,0,0,1,3], [0,0,0,0,0] ]) 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_rowspace = M.rowspace() M_columnspace = M.columnspace() print('輸出列空間的向量之線性組和= row space= \n', M_rowspace) print('輸出行空間的向量之線性組和= column space= \n', M_columnspace) 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() print('線性轉換後有壓縮空間 = 核空間向量集合 = null space=\n', M_nullsapce)