Reconstruction of matrices from submatrices
Reconstruction of matrices from submatrices
复制标题
从子矩阵重建矩阵
作者：
G. Kós;P. Ligeti;P. Sziklai
对于n x n符号的任意矩阵A，请考虑通过删除n-k行和n-k列获得的大小k x k。 。在对称和非对称情况下。
For an arbitrary matrix A of n x n symbols, consider its submatrices of size k x k, obtained by deleting n―k rows and n―k columns. Optionally, the deleted rows and columns can be selected symmetrically or independently. We consider the problem of whether these multisets determine matrix A. Following the ideas of Krasikov and Roditty in the reconstruction of sequences from subsequences, we replace the multiset by the sum of submatrices. For k > cn 2/3 we prove that the matrix A is determined by the sum of the k x k submatrices, both in the symmetric and in the nonsymmetric cases.