s*******y
发帖数: 558 | 1 给定一个矩阵 X_mxn, where n < m, 请问如何构建一个orthogonal
matrix Q such that QX = X.
如果rank(X) = m-1, 会有不同么?
谢谢了 | H****h
发帖数: 1037 | 2 Let Q=I_m.
【在 s*******y 的大作中提到】
: 给定一个矩阵 X_mxn, where n < m, 请问如何构建一个orthogonal
: matrix Q such that QX = X.
: 如果rank(X) = m-1, 会有不同么?
: 谢谢了
| s*******y
发帖数: 558 | 3 yes, this is obvious.
I am looking for other orthogonal matrices
that are not identity.
【在 H****h 的大作中提到】
: Let Q=I_m.
| m****n
发帖数: 45 | 4
If rank(X)=m-1, then n=m-1.
QX=X contains m*(m-1)independent equations for the entries of Q.
But a m-by-m orthogonal matrix only has m*(m-1)/2 freedom.
In this case, I think you probabily can't find a nontrivial Q as a solution.
【在 s*******y 的大作中提到】
: 给定一个矩阵 X_mxn, where n < m, 请问如何构建一个orthogonal
: matrix Q such that QX = X.
: 如果rank(X) = m-1, 会有不同么?
: 谢谢了
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