TL;DR
This paper extends classical theorems to symmetric matrix systems, providing a method to prepare analytic and smooth symmetric systems that vanish at finite order, enhancing understanding of their structure.
Contribution
It introduces a symmetric version of the Weierstrass and Malgrange preparation theorems for matrix-valued systems, a novel generalization in the field.
Findings
Established symmetric preparation theorems for analytic systems
Extended theorems to smooth symmetric systems
Proved finite order vanishing for these systems
Abstract
In this paper we generalize the Weierstrass and Malgrange preparation theorems to the symmetric matrix valued case, proving symmetric preparation of analytic and smooth symmetric systems that vanish of finite order.
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Taxonomy
TopicsPolynomial and algebraic computation · Matrix Theory and Algorithms · Holomorphic and Operator Theory