The matrix is orthogonal if QQT=I (T=transpose)
Given ATA=BTB (T=transpose)
show that there exist an orthogonal matrix Q such that A=QB
?????
prove of orthogonal matrix
2012-07-04 7:48 am
回答 (2)
2012-07-05 12:43 am
✔ 最佳答案
Are the any other properties on A or B?Are they invertible? Are the diagonalizable?
2012-07-04 16:43:22 補充：
If A^{-1} exists, then
A = A^{-T}A^{T}A = A^{-T}B^{T}B
Let Q = A^{-T}B^{T}, now QQ^{T} =
A^{-T}B^{T}(A^{-T}B^{T})^{T}
= A^{-T}B^{T}BA^{-1}
= A^{-T}A^{T}AA^{-1}
= I
Therefore Q is orthogonal.
2012-07-04 5:48 pm
A and B is non singular matrix
收錄日期: 2021-04-23 18:31:13
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120703000051KK00744