Properties of sub-matrices of Sylvester matrices and triangular toeplitz matrices
Yousong Luo, Robin Hill, Uwe Schwerdtfeger
TL;DR
This paper explores the relationships among sub-matrices of Sylvester and triangular Toeplitz matrices, highlighting Hill's identity and its significance in optimal control applications.
Contribution
It discovers and proves new relations among sub-matrices of Sylvester and triangular Toeplitz matrices, including Hill's identity.
Findings
Hill's identity is established and proven.
Relations among sub-matrices are characterized.
Applications in optimal control are discussed.
Abstract
In this note we discover and prove some interesting and important relations among sub-matrices of Sylvester matrices and triangular toeplitz matrices. The main result is Hill's identity discovered by R. D. Hill which has an important application in optimal control problems.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Optimization Algorithms Research · graph theory and CDMA systems