Talk:Triple product

Pseudovectors?

The stuff about pseudovectors needs to be reviewed by someone who understands it. I think the notation could be improved to clarify things. It is not clear to me what the significance of this is. Dhollm 12:59, 6 May 2007 (UTC)

Can you please clarify what you feel needs to be improved? Also, what do you miss in terms of significance? Thanks. Edgerck 19:19, 6 May 2007 (UTC)

Note: I partly reversed your cuts, which made the article clash with other wikipedia references. I hope to also have made it clearer. Edgerck 19:27, 6 May 2007 (UTC)

index notation

i think it might be helpful if you included the index notation for the triple product —Preceding unsigned comment added by 128.95.141.33 (talk) 02:10, 26 October 2007 (UTC)

I agree. I believe it can be useful (although the BAC-CAB rule is clear enough), but I can't do it immediately. Paolo.dL (talk) 20:25, 16 January 2008 (UTC)

The indexes with the Levi Civita notation in the final part of the page are wrong. in fact Ax(BxC)= epsilon_ijk a_j epsilon_klm b_l c_m = epsilon_kij epsilon_klm a_j b_l c_m . This change in indexes is in reality a change in the sign of the solution.

Lorebene (talk) 17:00, 27 September 2011 (UTC)

That agrees with Cross product. —Ben FrantzDale (talk) 15:26, 28 September 2011 (UTC)

Pseudovectors and pseudoscalars

I rewrote the sentences about pseudovectors and pseudoscalars. In my opinion, they were not clear, and one of them was wrong (the "if and only if" in scalar vector product). Please check and let me know if you agree and if you like them. Paolo.dL (talk) 23:42, 16 January 2008 (UTC)

Lagrange's Formula

Lagrange's formula is currently internally linked, but this leads to a disambiguation page, which in turn leads back to the section on this page. It's completely circular, but I'm not sure what the intention was. Warrickball (talk) 21:24, 12 May 2008 (UTC)

It is just a way to warn the reader that "Lagrange's formula" is ambiguous: it does not refer only to triple product expansion. This is useful information, based on which people may choose to use "triple product expansion", rather than "Lagrange's formula", to avoid ambiguity. Paolo.dL (talk) 07:51, 14 May 2008 (UTC)

Erroneous Equation

The following was included as a property of triple-products:

"There is also this property of triple products:

$\mathbf{a}\cdot(\mathbf{b}\times \mathbf{c})=(\mathbf{a}\times \mathbf{b})\times (\mathbf{a}\times \mathbf{c})$

" It cannot be correct as the left-hand side of the equality is a scalar and the right-hand side is a vector. Perhaps someone knows what was intended?

The original equation (the correct one), was:

$(\mathbf{a}\cdot(\mathbf{b}\times \mathbf{c})) \mathbf{a}=(\mathbf{a}\times \mathbf{b})\times (\mathbf{a}\times \mathbf{c})$

In fact, there was a fun succession of edits, the first one removed the first opening parenthesis, the next removed the closing parenthesis next to 'a', and at last, Bjordan555 removed the 'a' from it... I don't know why this happened. I've undone the changes and corrected it again. I've changed the parenthesis for brackets to clarify it.

Another notation

Can't square brackets be used for the triple product?

$[\mathbf{a}, \mathbf{b}, \mathbf{c}] := \mathbf{a} \cdot \mathbf{b} \times \mathbf{c}$

...or is it:

$[\mathbf{a}, \mathbf{b}, \mathbf{c}] := \mathbf{a} \times \mathbf{b} \cdot \mathbf{c}$

(The last is used in Rutherford, D. E. (1965). Vector Methods. University Mathematical Texts. Oliver and Boyd Ltd., Edinburgh. ) Alksentrs (talk) 14:37, 15 June 2009 (UTC)

As in Russian education, the following is considered true: $[\mathbf{a}, \mathbf{b}, \mathbf{c}] := (\mathbf{a} \cdot [\mathbf{b} \times \mathbf{c}])$. As one has to make two different multiplications - one "cross product", one "dot product" - this is called mixed product.--Q0k (talk) 22:03, 16 November 2009 (UTC)

scalar, vector - and where is mixed ?

What is $\mathbf a \cdot [\mathbf b \times \mathbf c]$? What is $\mathbf a \times (\mathbf b \cdot \mathbf c)$? --Q0k (talk) 04:48, 15 November 2009 (UTC)

Pseudoscalars???

Under the section Scalar or pseudoscalar the article reads:

"The scalar triple product typically returns a pseudoscalar, although a pseudoscalar is equivalent to a (true) scalar if the (mathematical) orientation of the coordinate system is selected in advance and fixed."

No. The scalar triple product is a mathematical function, not a computer subroutine, and as such it doesn't "return" anything; it takes values. More important, it doesn't have "typical" behavior: It *always* takes a scalar value, defined as the determinant of the matrix (a b c), where a, b, and c form an ordered triple of vectors in R³.

If someone wants to write a different article about some variant of the scalar triple product used in physics, that's one thing. But it's not appropriate to confuse readers about a very standard mathematical function. This entire section should be removed from this article.Daqu (talk) 22:20, 25 September 2010 (UTC)

You are right about "return". As a programmer it makes sense to me but it's not a mathematical term, so I've rewritten it using more mathematical language there and further down. It's still making a valid point, hopefully more clearly now, so there's no need to remove it.--JohnBlackburne^words_deeds 22:29, 25 September 2010 (UTC)

I believe that articles about programming should be written by people who are expert in the subject of programming. Articles about math, by people expert in math. No one expert in math has ever called the value of the triple scalar product a pseudoscalar. I don't consider a false statement to be a "valid point". The value of a triple scalar product is a number, not a "pseudoscalar".Daqu (talk) 05:16, 26 September 2010 (UTC)

It makes sense to me, but could be clearer so I've rewritten it. The pseudoscalar is a valid and well defined concept in maths and physics, and this is a good example of it. If a reader is not familiar with it they can follow some of the links which go into it in far more detail than I think's appropriate for this article, but it's good to mention it here to fit this product into its various applications and generalisations. --JohnBlackburne^words_deeds 10:13, 26 September 2010 (UTC)

Pseudoscalar is a well-defined concept in math/physics. Actually, a computer scientist might be more prone than a mathematician to call it a scalar (it's just a float; why give it a fancy type?). If you are working with matrices of scalars, then yea, it's a scalar (as you said, it's just the determinant of the matrix), but if you are using a richer algebra that accounts for more than one coordinate system, then it can't be just a scalar: instead of a matrix you have a tensor and so instead of the determinant you use the Levi-Civita symbol which itself is not a tensor but a pseudotensor again giving you a pseudoscalar. —Ben FrantzDale (talk) 22:08, 26 September 2010 (UTC)