关于一般相关高斯矩阵的最小特征值
On the Smallest Eigenvalue of General correlated Gaussian Matrices
摘要：
本文研究了一般相关高斯随机矩阵的谱的行为，这些矩阵的列是零均值独立向量，但具有不同的相关性，在特定的制度下，它们的列数和行数以相同的速度无限增长。这项工作的动机，特别是从统计信号处理和无线通信，这种矩阵自然出现的应用。按照文[1]中提出的方法，我们证明了在某些特定条件下，一般相关高斯矩阵的最小奇异值几乎必定远离零。
英文摘要：
This paper investigates the behaviour of the spectrum of generally correlated Gaussian random matrices whose columns are zero-mean independent vectors but have different correlations, under the specific regime where the number of their columns and that of their rows grow at infinity with the same pace. This work is, in particular, motivated by applications from statistical signal processing and wireless communications, where this kind of matrices naturally arise. Following the approach proposed in [1], we prove that under some specific conditions, the smallest singular value of generally correlated Gaussian matrices is almost surely away from zero.
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