Exploring Toeplitz, Circulant, and Hankel Matrices: Algebraic Structures and Field Properties with a Focus on Circulant Matrices

Abstract

This abstract provides an overview of the discussed topics related to Toeplitz matrices, Circulant matrices, Hankel matrices, and their connections to algebraic structures. Additionally, the abstract introduces the exploration of Group, Ring, and Field properties with a focus on the Field Properties of Circulant Matrices. Furthermore, the concept of Eigenvalues in Circulant Matrices is introduced, shedding light on the intrinsic characteristics of these matrices. The abstract concludes by highlighting the visualization aspect through the Graph of column vectors of Circulant Matrices, emphasizing the significance of graphical representations in understanding the matrix properties. Overall, the abstract encapsulates a comprehensive exploration of mathematical concepts and their applications, showcasing the interconnectedness of linear algebra and algebraic structures.