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#1 macosxnerd101  Icon User is online

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Hypergraphs, Hypermatrices, and Tensors

Post icon  Posted 26 January 2014 - 08:29 PM

I'm starting to weed through a paper on The Spectra of Hypergraphs for my class on Hypergraph Algorithms. Given the nature of the hyperedges, it isn't easy to use an n x n Adjacency Matrix to describe hypergraphs. I've been weeding through some multilinear algebra and abstract algebra with respect to modules (more or less, vector spaces over rings), and tensors (products of modules, in which the product space is a module). I'm about to delve into the hyperdeterminant.

Has anyone worked in this area before? Conceptualizing this is hard, with so few examples out there. Does anyone have any suggestions? Any thoughts in general?

I have found this introduction to tensors, Definition 2.2.9 of the adjacency hypermatrix here, and Abstract Algebra by Dummit and Foote to be helpful, in case anyone else is interested in general.

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Replies To: Hypergraphs, Hypermatrices, and Tensors

#2 macosxnerd101  Icon User is online

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Re: Hypergraphs, Hypermatrices, and Tensors

Posted 26 January 2014 - 10:22 PM

I came across a Tensors for Dummies PDF in doing some digging. It's been quite helpful in just the first couple pages. For those with some math but not a ton of physics, this is probably a better introduction. Most of the Tensor material you'll find out there throws a lot of notation at you without explaining it.
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