Re: [線代] 幫忙解一下!!
※ 引述《a520683 (小YA)》之銘言：
: Prove that the produce of two upper triangular matrix is upper triangular.
令A,B均為上三角 C=AB
則對所有i>j, a_ij=b_ij=0 (上三角定義)
要證對所有i>j, c_ij=0
給定i > j
n
c_ij = Σ a_ik * b_kj
k=1
= a_ii * b_ij + ... + a_in * b_nj (因為a_i1 = ... = a_i(i-1) = 0)
= 0 (因為b_ij = ... = b_nj = 0)
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