A NOTE ON SYMMETRIC k-TRIDIAGONAL MATRIX FAMILY AND THE FIBONACCI NUMBERS

ON TENSOR PRODUCT DECOMPOSITION OF $k$-TRIDIAGONAL TOEPLITZ MATRICES

“…In Subsection 3.1, we present some corollaries, which are obtained from Theorem 1. Some of the corollaries imply the theorem and the proposition that were proved in [13], however the corollaries in the present paper have simpler and more general expressions than in [13]. In Subsection 3.2, we show that Theorem 1 is used in order to reduce a computational complexity.…”

“…Let a = 1, d = 0, and m = 4 in (7). Then Corollary 6 corresponds to [13,Proposition 2]. As for Corollary 7, we have…”

“…In Section 2, we give a theorem of the decomposition via tensor product and show two examples. In Section 3, the decomposition is applied in order to simplify the theorem and the proposition in [13] and to reduce a computational complexity.…”

On Determinants of Tridiagonal Matrices With Alternating Pairs of 1' and -1' on the Diagonal Connected With Fibonacci Numbers

“…Many authors derived the similar types of matrices which determinants or permanents are related to Fibonacci numbers or different kinds of their generalizations, e. g. k-generalized Fibonacci numbers, see [5], [7] [2], [6], [9] and [11]. Now we turn our attention to the relation of determinants of special tridiagonal matrices with Fibonacci numbers.…”

ON A SEQUENCE OF TRIDIAGONAL MATRICES WHOSE DETERMINANTS ARE FIBONACCI NUMBERS $F_{n+1}$

“…Many authors derived the similar types of matrices which determinants are related to Fibonacci numbers or different kinds of their generalizations, e. g. k-generalized Fibonacci numbers, see [2], [4], [7], [6], [3], [8], [9] and [11]. Now we turn our attention to the relation of determinants of special tridiagonal matrices with Fibonacci numbers.…”