6
$\begingroup$

Is there a special name for an outer product of a vector with itself? Is it a special case of a Gramian? I've seen them a thousand times, but I have no idea if such product has a name.

Update: The case of outer product I'm talking about is $\vec{u}\vec{u}^T$ where $\vec{u}$ is a column vector.

Does is have a name in the form of something of $\vec{u}$?

Cheers!

$\endgroup$
3
  • $\begingroup$ The outer product of any vector with itself is always 0, since the outer product is skew symmetric. (EDIT: I would have made this a comment, but I don't have enough rep to do so on this stack exchange site ). $\endgroup$
    – Mikola
    May 25 '11 at 18:31
  • 1
    $\begingroup$ @Mikola: there are two things that get called the "outer product," and that's only one of them: see en.wikipedia.org/wiki/Outer_product . @Phonon: what definition of outer product are you working with? The coordinate one? $\endgroup$ May 25 '11 at 18:35
  • $\begingroup$ I updated my response. Thanks for the comments. $\endgroup$
    – Phonon
    May 25 '11 at 18:40
5
$\begingroup$

In statistics, we call it the "sample autocorrelation matrix", which is like an estimation of autocorrelation matrix based on observed samples.

$\endgroup$
1
  • $\begingroup$ I guess this is the closes to what I'm looking for. Thanks. $\endgroup$
    – Phonon
    May 27 '11 at 14:57
5
$\begingroup$

The result is a particular case of a dyadic tensor. Is that what you are looking for?

$\endgroup$

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.