Convergence of empirical spectral distributions of large dimensional quaternion sample covariance matrices
Convergence of empirical spectral distributions of large dimensional quaternion sample covariance matrices
复制标题
DOI：
10.1007/s10463-015-0514-0
复制
发表时间：
2013-10
影响因子：
1
通讯作者：
Huiqin Li;Z. Bai;Jiang Hu
中科院分区：
文献类型：
--
作者：
Huiqin Li;Z. Bai;Jiang Hu
在本文中，我们建立了四元数样本协方差矩阵的经验谱分布的极限。受 Bai 和 Silverstein（大维随机矩阵的频谱分析，Springer，纽约，2010）以及 Marčenko 和 Pastur（Matematicheskii Sb，114：507-536，1967）的启发，我们可以将实数或复数样本协方差矩阵的结果扩展到四元数情况。假设 是一个四元数随机矩阵。对于每个条目，条目都是具有共同均值和方差的独立随机四元数变量。结果表明，四元数样本协方差矩阵的经验谱分布收敛于 Marčenko–Pastur 定律：
In this paper, we establish the limit of empirical spectral distributions of quaternion sample covariance matrices. Motivated by Bai and Silverstein (Spectral analysis of large dimensional random matrices, Springer, New York, 2010) and Marčenko and Pastur (Matematicheskii Sb, 114:507–536, 1967), we can extend the results of the real or complex sample covariance matrix to the quaternion case. Supposeis a quaternion random matrix. For each, the entriesare independent random quaternion variables with a common meanand variance. It is shown that the empirical spectral distribution of the quaternion sample covariance matrixconverges to the Marčenko–Pastur law as,and.