摘要
设Ω是一个任意域,屠伯壎先生证明了定理:域Ω上的任一方阵必可分解为个数不超过4个的、域Ω上的对称阵的乘积。本文进一步证明了定理:域Ω(特征P≠2)上的任一方阵必可分解为域Ω上的两个对称阵的乘积,且其中之一为可逆的,定理的证明是构造性的。
Let Ω be a field. Mr. Tu Boxun has proved the theorem that every matrix on Ω is the product of no more than four symmetric matrices.The purpose of this paper lies in proving the following:Theorem. Every square matrix onΩ(p≠2)is the product of two symmetric matrices, and one of them is invertible.The proof is constructive.
关键词
域
方阵
对称阵
伴随阵
field, square matrix, symmetric matrix, adjoint matrix, invariant factor
