For a class of real Toeplitz P-matrix, a list of position 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 of order 4 have completion under certain condition. Some sufficient conditions that guarantee an n-by-n partial position symmetric Toeplitz Pmatrix has completion were given.
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