稀疏循环矩阵的奇异性是NP-完全的
Singularity of Sparse Circulant Matrices is NP-complete
摘要：
通过Karp约化证明了判定$(2^n - 1) \times (2^n - 1)$稀疏循环矩阵的奇异性（SC问题）是NP完全的。我们只能隐式地写它们，通过指示$2 + n(n + 1)/2$的值，最终第一行的非零项，并可以用它们进行所有矩阵运算。位置是$0, 1, 2^{i} + 2^{j}$。复杂度参数是$n$。Mulmuley关于矩阵秩\cite{Mulmuley87}的工作使得SC在3，000个且不断增长的NP完全问题中脱颖而出。
英文摘要：
It is shown by Karp reduction that deciding the singularity of $(2^n - 1) \times (2^n - 1)$ sparse circulant matrices (SC problem) is NP-complete. We can write them only implicitly, by indicating values of the $2 + n(n + 1)/2$ eventually nonzero entries of the first row and can make all matrix operations with them. The positions are $0, 1, 2^{i} + 2^{j}$. The complexity parameter is $n$. Mulmuley's work on the rank of matrices \cite{Mulmuley87} makes SC stand alone in a list of 3,000 and growing NP-complete problems.
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