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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!

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  • $\begingroup$ 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, 2011 at 18:31
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    $\begingroup$ @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, 2011 at 18:35
  • $\begingroup$ I updated my response. Thanks for the comments. $\endgroup$
    – Phonon
    May 25, 2011 at 18:40

2 Answers 2

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

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  • $\begingroup$ I guess this is the closes to what I'm looking for. Thanks. $\endgroup$
    – Phonon
    May 27, 2011 at 14:57
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The result is a particular case of a dyadic tensor. Is that what you are looking for?

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