Mika Mattila

On the positive definiteness and eigenvalues of meet and join matrices

In this paper we study the positive definiteness of meet and join matrices using a novel approach. When the set

On the eigenvalues of combined meet and join matrices

S_n

Studying the singularity of LCM-type matrices via semilattice structures and their Möbius functions

is meet closed, we give a sufficient and necessary condition for the positive definiteness of the matrix

Some properties of row-adjusted meet and join matrices

(S_n)_f

On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix

. From this condition we obtain some sufficient conditions for positive definiteness as corollaries. We also use graph theory and show that by making some graph theoretic assumptions on the set

A lattice-theoretic approach to the Bourque-Ligh conjecture

S_n

Perpendicularity in an Abelian Group

we are able to reduce the assumptions on the function

Maximal perpendicularity in certain Abelian groups

f

Bounds for sine and cosine via eigenvalue estimation

while still preserving the positive definiteness of the matrix

ON THE EIGENVALUES OF CERTAIN NUMBER-THEORETIC MATRICES

(S_n)_f