Re: [中學] 請問矩陣證明
: 請問21題第一小題要怎麼證明www
令 u = [a b c]^T ， v = [x,y,z]^T
u_1 = a, u_2 = b, u_3 = c
v_1 = x, v_2 = y, v_3 = z
則 u v^T = A
3
又 (A^2)_{ij} = Σ A_{ik} A_{kj}
k=1
= (u_i v)^T (v_j u)
= (v^T u)(u_i v_j)
= (xa+yb+zc) (u v^T)_{ij}
= (xa+yb+zc) A_{ij}
因此 A^2 = (xa+yz+zc) A
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 114.46.224.164
※ 文章網址: https://www.ptt.cc/bbs/Math/M.1429357194.A.4FD.html
推
04/18 23:23, , 1F
04/18 23:23, 1F
→
04/18 23:28, , 2F
04/18 23:28, 2F
推
04/18 23:46, , 3F
04/18 23:46, 3F
討論串 (同標題文章)
