Talk:Linear algebra
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So what other stuff has the structure of a linear space but has elements that are not real or complex numbers?
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
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
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 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
Linear algebraists, please help
The derivation of the maximum-likelihood estimator of the covariance matrix of a multivariate normal distribution is perhaps surprisingly subtle and elegant, involving the spectral theorem of linear algebra and the fact that it is sometimes better to view a scalar as the trace of a 1×1 matrix than as a mere scalar. See estimation of covariance matrices. Please help contribute a "linear algebraists' POV" to that article. Michael Hardy 20:20, 10 Sep 2004 (UTC)
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)
Useful Theorems of linear algebra
The statement about definite and semi-definite matrices is not correct as stated. Matrices should be assumed to be symmetric. Moreover, this is slightly off-topic: it is rather part of bilinear algebra rather than linear algebra.
The statement ``A non-zero matrix A with n rows and n columns is non-singular if there exists a matrix B that satisfies AB = BA = I where I is the identity matrix is much more a definition than a theorem
In my opinion, the main non-trivial result of linear algebra says that the Dimension of a vector space is well defined: Theorem: If a vector space has two bases, then they have the same cardinality.