Convolution of Matrices and Positivity Preservation
Research Paper#Matrix Analysis, Convolution, Positivity🔬 Research|Analyzed: Jan 3, 2026 06:30•
Published: Dec 31, 2025 02:47
•1 min read
•ArXivAnalysis
This paper explores convolution as a functional operation on matrices, extending classical theories of positivity preservation. It establishes connections to Cayley-Hamilton theory, the Bruhat order, and other mathematical concepts, offering a novel perspective on matrix transforms and their properties. The work's significance lies in its potential to advance understanding of matrix analysis and its applications.
Key Takeaways
- •Convolution is formulated as a functional operation on matrices.
- •The framework preserves positivity through a matrix transform.
- •Connections are established with classical theories like Pólya--Szegő and Schoenberg.
- •A Cayley--Hamilton-type theory and a novel polynomial-matrix identity are central to the transform's structure.
- •A link between convolution and the Bruhat order is uncovered.
Reference / Citation
View Original"Convolution defines a matrix transform that preserves positivity."