# Talk:Linear algebra

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## Finite fields

In computational number theory you sometimes get people doing linear algebra on matrices made out of integers modulo a prime. Often the prime is 2, but larger ones are also used.

My guess is the elements have to be from a ring or maybe a field. Anyway something with a group operation on the whole set, another group operation on the set except for identity of the first group, distributive law between the two group operations.

Anything to do with finite fields? --Damian Yerrick

## Fields and rings

You can do linear algebra over any field. If you're working with rings, they're called modules. Modules share many of the properties of vector spaces, but certain important basic facts are no longer true (the term dimension doesn't make much sense anymore, as bases may not have the same cardinality.) --Seb

## Striking (wrong) example

Quoted from the main page:

A vector space, as a purely abstract concept about which we prove theorems, is part of abstract algebra, and well integrated into this field. Some striking examples of this are the group of invertible linear maps or matrices,

This is truly a striking example :-)

Toby Bartels and I are going to correct this and I think we're also going to write about linear algebra over a rig (algebra) (this is not a typo!). -- Miguel

@Miguel @Toby Bartels No rig?

## How did Hamilton name vectors?

Quote from the article: "In 1843, William Rowan Hamilton (from whom the term vector stems) discovered the quaternions."

Huh? I didn't find the answer on a quick perusal of the William Rowan Hamilton article either. I didn't see it in quaternions either. It sounds like an interesting story, but what (or where) is the story? Spalding 18:25, Oct 4, 2004 (UTC)

Well, it's there now. Lowellian (talk)[[]] 23:05, Oct 7, 2004 (UTC)

## Equivalent statements for square matrices

This is not an elegant section: it feels slightly like a dumping ground for a bunch of facts. Did anyone else have the same feeling? (Yiliu60)

Yes. Jitse Niesen (talk) 6 July 2005 09:21 (UTC)

## Vote for new external link

Here is my site with linear algebra example problems. Someone please put this link in the external links section if you think it's helpful and relevant. Tbsmith

http://www.exampleproblems.com/wiki/index.php/Linear_Algebra