User:Peter Stalin

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Introduction[edit]

Hi.

I'm just a mathematics student. I don't plan to make any major edits or articles, I just want a place to have my small edits be counted up as random contributions.

Well, unless some major mathematical topic is missing.

Thanks, Peter Stalin 04:33, 27 March 2007 (UTC)


Preparing up a complete set of residues mod m page[edit]

Here's an outline before I start making the article later this week:

-Definition

-Representations --Examples of general representations --Least Absolute residues --Least Positive residues

-Some theorems

-Reduced residue classes

-Some theorems of this too

I still need someplace to mention the 'residue equivalence class' and the applications to group theory in this outline. Peter Stalin 14:13, 28 March 2007 (UTC)

Making a redirect Muller-Traub

Another outline[edit]

I don't feel like doing this atm:

In [linear algebra], a matrix A \in \mathbb{C}^{n\times n} has a displacement rank r if it satisfies a (Sylvester) displacement equation

EA-AF=GH^*

Where G,H\in\mathbb{C}^{n\times r} and E,F are called displacement matrices.

Such matrices are useful in defining and categorizing other structured matrices, for example, we can categorize the various matrix structures of the resultant matrix A by the following choices for E,F,G and H

Structure E F G H
Cauchy Matrix D_t D_s g h
Cauchy Matrix D_t D_s
Cauchy Matrix D_t D_s

Where g,h are vectors, D_t,D_s are diagonal matrices,