Jordan Algebras of Symmetric Matrices
Arthur Bik, Henrik Eisenmann, Bernd Sturmfels
TL;DR
This paper investigates Jordan algebras formed by symmetric matrices, classifies low-dimensional cases, and explores their geometric properties within the Grassmannian.
Contribution
It provides a classification of low-dimensional Jordan algebras of symmetric matrices and analyzes their geometric loci in the Grassmannian.
Findings
Classification of low-dimensional Jordan algebras of symmetric matrices
Description of Jordan loci in the Grassmannian
Insights into the structure of reciprocal linear spaces
Abstract
We study linear spaces of symmetric matrices whose reciprocal is also a linear space. These are Jordan algebras. We classify such algebras in low dimensions, and we study the associated Jordan loci in the Grassmannian.
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Taxonomy
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms · graph theory and CDMA systems