秩1矩阵的性质及其在统计学中的应用

摘要

n维列向量x与xT的乘积，为秩为1的矩阵xxT。本文对这种秩1矩阵的结构、乘法运算、特征值与特征向量等性质进行了讨论，结合这些性质重点讨论了秩1矩阵在统计学中的应用。Rank 1 matrices is the product of the n dimensional column vectors x and xT. This paper discussed some properties of the matrices with rank 1, like the structure, multiplication, eigenvalues and eigenvectors etc., and further analyzed the applications of the matrices applied in Statistics.