行列式行列对换,行列式的值不变 21a22 n12a22 ar 引理 一个排列的逆序对数,在对换排列中两个数的位置时,奇偶性改变。 N(1i2…i…i…in)=N(i2………in)+奇数 413562:逆序对:(41),(43),(42),(32),(6,2) ↓ 415362:逆序对:(4,1),(43),(42),(32),(6,2),(53)pê E￾ŒÆ£Á‘¤ 1ª 1ª5Ÿ 1ª1醧1ªŠØC Dn =          a11 a12 ⋅ ⋅ ⋅ a1n a21 a22 ⋅ ⋅ ⋅ a2n . . . . . . . . . . . . an1 an2 ⋅ ⋅ ⋅ ann          =          a11 a21 ⋅ ⋅ ⋅ an1 a12 a22 ⋅ ⋅ ⋅ an2 . . . . . . . . . . . . a1n a2n ⋅ ⋅ ⋅ ann          = D T n Ún ‡ü_Séê§3é†ü¥ü‡ê ž§Ûó5UC" = N ( i1 i2 ⋅ ⋅ ⋅ ij ⋅ ⋅ ⋅ ik ⋅ ⋅ ⋅ in ) = N ( i1 i2 ⋅ ⋅ ⋅ ik ⋅ ⋅ ⋅ ij ⋅ ⋅ ⋅ in ) + Ûê 4 1 3 5 6 2 µ_Séµ(4, 1),(4, 3),(4, 2),(3, 2),(6, 2) ⇓ 4 1 5 3 6 2 µ_Séµ(4, 1),(4, 3),(4, 2),(3, 2),(6, 2),(5, 3)