Durmuş Bozkurt

Determinants and Inverses of Circulant Matrices with Jacobsthal and Jacobsthal-Lucas Numbers

Abstract Let n ⩾ 3 and let J n ≔ circ ( J 1 , J 2 , … , J n ) and j n ≔ circ ( j 0 , j 1 , … , j n - 1 ) be the n × n circulant matrices associated with the Jacobsthal numbers J 1 , … , J n and the Jacobsthal–Lucas numbers j 0 , … , j n - 1 , respectively. The determinants and the inverses of J n and j n are obtained in terms of J 1 , … , J n and j 1 , … , j n - 1 , respectively.

Determinants and inverses of r-circulant matrices associated with a number sequence

Let be the -circulant matrix associated with the numbers defined by the recursive relation with initial conditions and , where and We obtain some formulas for the determinants and inverses of . Some bounds for spectral norms of are obtained as applications.

Positive integer powers for one type of odd order circulant matrices

article i nfo abstract In this study we derive the general expression for the entries of the qth power q 2 N for

On the spectral norms of the matrices connected to integer number sequences

In this paper, we compute the spectral norms of the matrices related with integer sequences and we give two examples related with Fibonacci, Lucas, Pell and Perrin numbers.

On the l p norms of cauchy-toelitz matrices

In this study, we have found an upper and lower bounds for the l p norm (1 < p < ∞) of Cauchy-Toeplitz matrix in the form . Moreover, we have given a conjecture for the l pq (1 ≤ p,q ≤ ∞)norm of this matrix.

Bounds on the Distance Energy and the Distance Estrada Index of Strongly Quotient Graphs

The notion of strongly quotient graph (SQG) was introduced by Adiga et al. (2007). In this paper, we obtain some better results for the distance energy and the distance Estrada index of any connected strongly quotient graph (CSQG) as well as some relations between the distance Estrada index and the distance energy. We also present some bounds for the distance energy and the distance Estrada index of CSQG whose diameter does not exceed two. Additionally, we show that our results improve most of the results obtained by Gungor and Bozkurt (2009) and Zaferani (2008).

BOUNDS FOR THE DISTANCE ESTRADA INDEX OF GRAPHS

The D-eigenvalues {\mu}_1,{\mu}_2,...,{\mu}_{n} of a connected graph G are the eigenvalues of its distance matrix. The distance Estrada index of G is defined in [15] as DEE=DEE(G)=\Sigma_{i=1}^n e^{{\mu}_{i}} In this paper, we give better lower bounds for the distance Estrada index of any connected graph as well as some relations between DEE(G) and the distance energy.

A note on bound for norms of Cauchy–Hankel matrices

We determine bounds for the spectral and p norm of Cauchy–Hankel matrices of the form Hn=[1/(g+h(i+j))]ni,j=1≡ ([1/(g+kh)]ni,j=1), k=0, 1,…, n –1, where k is defined by i+j=k (mod n). Copyright

Another proof of Pell identities by using the determinant of tridiagonal matrix

Abstract In this paper, another proof of Pell identities is presented by using the determinant of tridiagonal matrix. It is calculated via the Laplace expansion.

On the complex factorization of the Lucas sequence

In this paper, firstly we present a connection between determinants of tridiagonal matrices and the Lucas sequence. Secondly, we obtain the complex factorization of Lucas sequence by considering how the Lucas sequence can be connected to Chebyshev polynomials by determinants of a sequence of matrices.