2021/09/13 by Ben O’Neill, O'Neill, Ben
Chemistry · Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Spectroscopy and Chemometric Analyses #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2109.05814
openalex publication_date 2021/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper examines the properties of real symmetric square matrices with a constant value for the main diagonal elements and another constant value for all off-diagonal elements. This matrix form is a simple subclass of circulant matrices, which is a subclass of Toeplitz matrices. It encompasses other useful matrices such as the centering matrix and the equicorrelation matrix, which arise in statistical applications. We examine the general form of this class of matrices and derive its eigendecomposition and other important properties. We use this as a basis to look at the properties of the centering matrix and the equicorrelation matrix, and various statistics that use these matrices.