关于一些特殊r-循环矩阵的谱范数

摘要

利用矩阵的一般理论和Gamma函数的性质,给出了r-循环矩阵A=Cr(C0n,1/2C1n,…,1/nCnn-1)和B=Cr(0,C1n,…,(n-1)Cnn-1)的谱范数的上界与下界,这里Ckn是二项式系数；得到了矩阵A与B的Kronecker积与Hadamard积的谱范数的一些界.%By the general theory of matrix and some properties of Gamma function, the upper and lower bounds for the spectral norms of r-circulant matrices A=Cr (C/n,1/3C1/n,…,1/n-Cn/n-1 ) and B=Cr(0,C1/n,…,(n - 1)Cn/n-1) are given, where Cj is the binomial coefficient. Some bounds for the spectral norms of Hadamard and Kronecker products of these matrices are obtained.