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I was watching this video: https://www.youtube.com/watch?v=RDkwklFGMfo

And the professor is talking about the inner product... then he brings up the "canonical" representation of the inner product in R^N.

What, specifically, does he mean? I see it a lot in matrix talk, but I'm never really sure what they mean.

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    $\begingroup$ Canonical in this sense means "standard" $\endgroup$ – Oria Gruber Sep 23 '15 at 21:51
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It is not the usual terminology. "Canonical" has a well established use in linear algebra as a construction that is independent of a basis, or at least invariant with respect to different choices of basis. The thing in the lecture slides (around 25min in the video) is ordinarily called the "standard" inner product associated to a basis, or the "Euclidean" inner product.

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