On linear transformations preserving at least one eigenvalue

On Zero-Preserving Linear Transformations

For an arbitrary subset I of IR and for a function f defined on I, the number of zeros of f on I will be denoted by ZI(f) . In this paper we attempt to characterize all linear transformations T taking a linear subspace W of C(I) into functions defined on J (I, J ⊆ IR) such that ZI(f) = ZJ (Tf) for all f ∈ W .

On One-Sided Ideals of Rings of Linear Transformations

Notes on graphs with least eigenvalue at least -2

A new proof concerning the determinant of the adjacency matrix of the line graph of a tree is presented and an invariant for line graphs, introduced by Cvetković and Lepović, with least eigenvalue at least −2 is revisited and given a new equivalent definition [D. Cvetković and M. Lepović. Cospectral graphs with least eigenvalue at least −2. Publ. Inst. Math., Nouv. Sér., 78(92):51–63, 2005.]. E...

Linear transformations preserving log-concavity

In this paper, we prove that the linear transformation yi = i ∑ j=0 ( m+ i n+ j ) xj , i = 0, 1, 2, . . . preserves the log-concavity property. © 2002 Elsevier Science Inc. All rights reserved.

Some Observations on Dirac Measure-Preserving Transformations and their Results

Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measure-preserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac ...