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.

翻译：本文件审视了真实对称平方矩阵的特性,其中主要对角元素的常值是真实对称平方矩阵的特性,所有非对角元素的常值是另一个常值。该矩阵表形式是一个简单的ircurlant矩阵子类,它是托普利茨矩阵的子类。它包括了其他有用的矩阵,如中央矩阵和在统计应用中产生的平衡关系矩阵。我们检查了这一类矩阵的一般形式,并得出了其等离子构造和其他重要属性。我们以此为基础查看中心矩阵和等离子矩阵的特性,以及使用这些矩阵的各种统计数据。