In this paper we approximated lower and upper bounds of the spectral norms of geometric circulant matrices with the generalized Fibonacci and hyperharmonic Fibonacci numbers.
In fact, in [11, 12], the authors calculated the spectral norms of the circulant matrices with the generalized Fibonacci and hyperharmonic Fibonacci numbers.
In [9], Yazlık and Taskara have presented new upper and lower bounds for the spectral norms of an r-circulant matrix with the generalized k-Horadam numbers.
In view of the above papers, we define a new circulant matrix which is called geometric circulant matrix and give upper and lower bounds for the spectral norms of this matrix with the generalized Fibonacci and hyperharmonic Fibonacci numbers by using the same method given in [3].
We observe that apparently the imaginary roots of a GRS are not determined by the real ones, contrarily to what happens with generalized Cartan matrices.
A matrix A ∈ R m × n is called generalized reflexive matrix with respect to the matrix pair ( P, Q ) if P A Q = A. The set of all m-by-n real generalized reflexive matrices with respect to a matrix pair ( P, Q ) is denoted by R r m × n ( P, Q ).
By a transitional design matrix and its adjoint matrix, a completely or partially inverse-based multi-input-multi-output (MIMO) decoupler with generalized form is presented to decouple the process into the specified open-loop process.
The primary analysis utilized logistic regression with generalized estimating equations with an exchangeable correlation matrix to compare the presence of detectable HIV-1 RNA in vaginal secretions across the three visits, using the pre-infection visit as the baseline.
For an involutory matrix R, we define the generalized centro-invertible matrices with respect to R to be those matrices A such that RAR="A−1.
with a i = ∏ j = 1 M σ i, j M, where the sequence { σ i, j } j = 1 M is the singular value of H i. U1 and U2 are unitary matrices of dimensions N1 × N1 and N2 × N2, respectively, D1 and D2 are generalized upper triangular matrices with equal diagonal elements, and † denotes the conjugate transpose.
