DETERMINANTS, INVERSES AND EIGENVALUES OF TWO SYMMETRIC POSITIVE DEFINITE MATRICES WITH PELL AND PELL-LUCAS NUMBERS
In this paper, we consider determinants, inverses and eigenvalues of symmetric matrices with Pell and Pell-Lucas numbers. As well-known numbers, the Pell and Pell-Lucas numbers play an important role in this research. For the determinants and inverses of symmetric matrices with Pell and Pell-Lucas numbers, we give their expressions respectively in the form of the Pell and Pell-Lucas numbers. Further, we give the general formulas of the solution of the linear equations with the Pell-min and Pell-Lucas-min symmetric matrix as the coefficient matrix, respectively. Meanwhile, we use the Geršgorin Theorem to give the range of eigenvalues.
determinant, inverse, eigenvalue, systems of linear equations, Pell number, Pell-Lucas number, symmetric matrices.