Re: [eigen] cross product with complex vectors |

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*To*: eigen <eigen@xxxxxxxxxxxxxxxxxxx>*Subject*: Re: [eigen] cross product with complex vectors*From*: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>*Date*: Mon, 16 Jul 2018 17:09:00 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025; h=mime-version:references:in-reply-to:from:date:message-id:subject:to; bh=MIQBsCs0qHrjwfvRrNAb1vkO++eVFZ3YnxYHVH1vvg4=; b=IHacoPuZNGB+v2ojVnoZrxQBaPk8GM260lqVQe+Sskm2rNQMoKnxNAkqBtDb5czX0R 08L/IKlIE7+tXplxYrjYi5kzDeOqOqCVVrUbH0YPalGtK+A+scABLgDjAe8BKjx5cYMZ oaf70Ou0aDkX8kiW4FHHPgk5mgGxPpK2XW13Cw2cZkpWVBRHV7s9uOt8G6bNZPMgQnGv rDcFp87kOU8t9vm5p7h73/85vVwSZA69SrUbjmOdHDCQ0zyW+u4Stmdes4Nd3Ui11gmL TMEOjHQfx5Xi1WSIMLmlTiApfxQsM0pLsVIhefAgkGd7QQXCFkZP4HGkoS/5+fLeEsMv +FBg==

On Mon, Jul 16, 2018 at 3:39 PM Orell Garten <orell.garten@xxxxxxxxxxxxxxxxxxxxx> wrote:

Hi

I was wondering whether the implementation of the cross product for

complex vectors [1] is correct.

Assume I have two vectors of type Vector3cd which hold a=(0,0,1) and

b=(0,1+i,0). I do a.cross(b) and would expect to get (-1-i,0,0) but get

(-1+i,0,0) as a result.

I think the formula in [1] should be (a + ib) x (c x id) = (a x c - b x

d) + i (a x d + b x c) but maybe I am wrong.

It would be great if somebody could provide some sanity check or the

reasoning behind [1].

For instance, see: https://math.stackexchange.com/questions/129227/cross-product-in-complex-vector-spaces

gael

Thanks for helping,

Orell

[1]

http://eigen.tuxfamily.org/dox/group__Geometry__Module.html#ga0024b44eca99cb7135887c2aaf319d28

**References**:**[eigen] cross product with complex vectors***From:*Orell Garten

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