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$$x^TAx+x^Tb+c=(x-h)^TA(x-h)+k$$ where $$h=-(A+A^T)^{-1}b$$ $$k=c-h^TAh$$

Determining $h$ and $k$ above is called "completing the square" and requires matrix addition, inversion, transposition, multiplication etc.

I am implementing algorithms (such as the above and others) in a generic way such that they can apply to any entity on which the requisite operations (addition, inversion, etc.) are defined.

I would call this library "matrix algebra" but I wondered whether there is a more abstract/generic name for "something that can be added, inverted, transposed, multiplied, etc.")?

Museful
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    I think you are looking for something like $*$-algebras. Nevertheless, the name 'matrix algebra' is a good name. – Berci Jan 25 '20 at 13:00

1 Answers1

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Yes this would be an example of geometric algebra. A matrix is just a representation of general algebraic /geometric objects like vectors, multivectors, dual multivectors etc..

Matko
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  • This should be a comment. Furthermore, what is a matrix? – PinkyWay Jul 02 '20 at 22:18
  • P.S. nisam downvoteala. (: – PinkyWay Jul 02 '20 at 22:24
  • Well the op says he is looking for algorithms for calculating these things. A think saying *algebra is not a good answer or comment in this case, don't think there are such general algorithms that would work. So I gave him an answer that's still quite abstract yet concrete in terms of computation. – Matko Jul 03 '20 at 08:47
  • I don't see why it should be a comment if it answers the question – Matko Jul 03 '20 at 08:48
  • And I think a matrix is what it is. Some set if rows and columns of numbers used to represent something, usually a linear operator.. – Matko Jul 03 '20 at 08:51
  • Neznam nevolim matrice, mozda Sam previse puta gledao film:) – Matko Jul 03 '20 at 08:52