Toeplitz P-阵的完成问题

Toeplitz P-matrix Completion Problem

部分阵的完成问题有着广泛的应用背景,本文从研究行列式符号的角度出发,主要讨论了P-阵的完成问题,指出三阶的部分位置对称Toep litz P-阵都有相应完成,给出了四阶Toep litz P-阵有相应完成的充分条件,在此基础上给出了n×n部分位置对称Toep litz P-阵有相应完成的一些模式.

For a class of real Toeplitz P-matrix,a list of positions in an n-by-n matrix (a pattern)is said to have Toeplitz P-matrix completion if every partial Toeplitz P-matrix that specifies exactly these positions can be completed to a Toeplitz P-matrix.It was discussed that the partial position symmetric Toeplitz p-matrix of order 3 have corresponding completion and the partial position symmetric Toeplitz P-matrix of order 4 have completion under certain condition.Some sufficient conditions that guarantee an n-by-n partial position symmetric Toeplitz P-matrix has completion were given.