推 gary27:收到線代區^^!140.134.242.144 08/24
※ 引述《Mimic54 (有感覺了ﰩ》之銘言：
: 請問一下 ㄧ個矩陣被稱作orthogonal
: 要有什麼條件阿??
A square matrix A is said to be orthogonal(正交) if AA'= A'A = I (definition)
A' is the transpose of A and I is a unit matrix
∵ A[A^(-1)] = [A^(-1)]A = I ---- A^(-1) is the inverse of A
∴ A'= [A^(-1)]
from the definitin
the product of the kth row of A and the kth column of A' = 1
the product of the kth row of A and the other columns of A' = 0
and in fact the kth row of A is equal to the kth column of A' (transpose)
so the inner product of the kth row vector with itself = 1 (normal)
and the inner product of the kth row vector with the other row vectors = 0
(each two row vectors are orthogonal)
so, the row(column) vectors of an orthogonal matrix are orthonormal
and the transpose of an orthogonal matrix is also orthogonal
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◆ From: 61.228.87.203
※ 編輯: youfly 來自: 61.228.87.203 (08/24 03:54)