In this paper it is shown that a partial Toeplitz positive definite matrix has a Toeplize positive definite completion if and only if the diagonals for the specified entries are 0, t, 2t, ¼, pt (in which the main diagonal is numbered 0). This gives a positive answer to the conjecture posed by C. R. Johnson.

References.

[1] Charles R. Johnson, Matrix completion problem: a survey, Proceedings of Symposia in Applied Mathematics, 40(1990), 171-198.

Footnotes:

¹ Joint work with Linzhang LU.