On computing the determinants and inverses of some special type of tridiagonal and constant-diagonals matrices

The determinants and inverses of some tridiagonal and constant-diagonals matrices are discussed in the paper. Linear recurrence equations of the second and higher orders which satisfy these determinants are presented here. In connection with these determinants new families of polynomials are defined. The relationships between these polynomials and normed Chebyshev polynomials of the first and second kind are investigated. Incidentally, a number of new identities for Chebyshev polynomials and some linear modifications of these polynomials are shown, as well as many new trigonometric identities and identities for Fibonacci and Lucas numbers.