[eigen] cross product with complex vectors

[Orell Garten]

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].

Thanks for helping,
Orell

[1]
http://eigen.tuxfamily.org/dox/group__Geometry__Module.html#ga0024b44eca99cb7135887c2aaf319d28

[Christoph Hertzberg]

Here is a related bugzilla entry:

http://eigen.tuxfamily.org/bz/show_bug.cgi?id=944

Short story: We can't just change our API here, but you can use this as
a workaround:

a.cross(b.conjugate());


Christoph

Post by Orell Garten
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].
Thanks for helping,
Orell
[1]
http://eigen.tuxfamily.org/dox/group__Geometry__Module.html#ga0024b44eca99cb7135887c2aaf319d28

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[Orell Garten]

Thanks for the quick answer. That helps for "mixed" vectors, if one does
not have an imaginary part.

Orell

Post by Christoph Hertzberg
http://eigen.tuxfamily.org/bz/show_bug.cgi?id=944
Short story: We can't just change our API here, but you can use this as
  a.cross(b.conjugate());
Christoph

Post by Orell Garten
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].
Thanks for helping,
Orell
[1]
http://eigen.tuxfamily.org/dox/group__Geometry__Module.html#ga0024b44eca99cb7135887c2aaf319d28

[Gael Guennebaud]

On Mon, Jul 16, 2018 at 3:39 PM Orell Garten <

Post by Orell Garten
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

Post by Orell Garten
Thanks for helping,
Orell
[1]
http://eigen.tuxfamily.org/dox/group__Geometry__Module.html#ga0024b44eca99cb7135887c2aaf319d28