On nonsingularity of circulant matrices
On nonsingularity of circulant matrices
复制标题
关于循环矩阵的非奇异性
DOI：
10.1016/j.laa.2020.12.010
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Zhangchi Chen
中科院分区：
文献类型：
--
作者：
Zhangchi Chen
摘要在通信理论与编码中，期望某些第一行有k个1和k+ 1个0的循环矩阵是非奇异的。我们证明了这样的矩阵总是非奇异的，当2 k+ 1是一个素数的幂，或两个不同的素数的产品。对于任何其他整数2k + 1，我们构造行列式为0的循环矩阵。最小奇异矩阵出现在2k + 1= 45时。这样的矩阵是奇异的可能性相当低，在这种情况下小于10− 4。
Abstract In Communication theory and Coding, it is expected that certain circulant matrices having k ones and k+ 1 zeros in the first row are nonsingular. We prove that such matrices are always nonsingular when 2 k+ 1 is either a power of a prime, or a product of two distinct primes. For any other integer 2 k+ 1 we construct circulant matrices having determinant 0. The smallest singular matrix appears when 2 k+ 1= 45. The possibility for such matrices to be singular is rather low, smaller than 10− 4 in this case.