A new product on 2x2 matrices
Linus Kramer, Peter Kramer, Vladimir Man'ko
TL;DR
This paper introduces a novel bilinear multiplication rule for 2x2 matrices that bridges the gap between standard and Hadamard matrix products, linking it to the hyperbolic motion group.
Contribution
It presents a new matrix multiplication method and explores its connection to hyperbolic geometry, offering insights into matrix algebra and geometric group theory.
Findings
Defines a new bilinear multiplication rule for 2x2 matrices
Establishes a relationship between this rule and the hyperbolic motion group
Provides mathematical properties and potential applications of the new product
Abstract
We study a bilinear multiplication rule on 2x2 matrices which is intermediate between the ordinary matrix product and the Hadamard matrix product, and we relate this to the hyperbolic motion group of the plane.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Tensor decomposition and applications · Matrix Theory and Algorithms