## Glas :## Re: [glas] arithmetic operations |

**From:** Andrew Lumsdaine (*lums_at_[hidden]*)

**Date:** 2005-10-28 08:14:46

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On Oct 28, 2005, at 2:23 AM, Karl Meerbergen wrote:

>

> It makes sense to use * for a product. But what does it mean for a

> vector? inner product, outer product, element wise product? And why

> prefer one to another?

I think we are agreeing here (?) -- my point is that * has no

mathematical meaning for vectors -- i.e., there is no mathematical

notion of a product between two vectors -- and hence, we should not

overload the meaning of operator* to be something new and

un-mathematical.

> To make the choice easier, we could assume that a vector is a column

> (as

> is always the case in linear algebra). In this case

> trans(x)*y = dot product

> x*trans(y) = outer product

> herm(x)*y = hermitian inner product

>

> This is probably the closest we can get to linear algebra notation.

Right. I think these all make perfect sense mathematically. I wasn't

suggesting to leave out the use of * altogether, but rather to use it

only in the ways that make sense mathematically. And to have it always

mean the same thing.

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