0
$\begingroup$

The set St(k, n), k < n, is called the Stiefel set.

does matrix X= $$ \left[ \begin{array}{ccc} 0&-{\sqrt 2}/2 \\ 0&{\sqrt 2}/2\\ 1&0 \end{array} \right] $$

belong to St(2,3)?

Im not really sure how to solve this. I dont understand what a stiefel set is and i've tried reading about it, but i still dont get it.

$\endgroup$
0
$\begingroup$

According to Wikipedia, and Wolfram Mathworld, a Stiefel manifold is a set of ordered $\ k$-tuples, $\ \left(v_1, v_2, \dots, v_k\right)\ $, of orthonormal vectors in $\ \mathbb{R}^n\ $. Presumably, this is what your expression $\ \text{St}(k,n)\ $ is intended to represent.

So if you treat your matrix $\ X\ $ as an ordered set of columns, then it will lie in $\ \text{St}(2,3)\ $ if and only it's an ordered set of $\ 2\ $ orthonormal columns in $\ \mathbb{R}^3\ $. Can you see whether or not that's true?

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ could you explain more please? $\endgroup$ – ELZP Feb 21 at 8:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.