Using techniques from algebraic topology we derive linear inequalities which relate the spectrum of a set of Hermitian matrices A1, . . . , Ar ∈ Cn×n with the spectrum of the sum A1 + · · ·+Ar. These extend eigenvalue inequalities due to Freede-Thompson and Horn for sums of eigenvalues of two Hermitian matrices.

In this work, we find the asymptotic formulas for sum of negative eigenvalues smaller than ?? (? > 0) a self-adjoint operator L defined by following differential expression ?(y)=?(p(x)y?(x))??Q(x)y(x) with boundary condition y(0) = 0 in space L2(0,?;H).

We consider graphs with two cut vertices joined by a path one or edges, and prove that there can be no quantum perfect state transfer between these vertices, unless the graph has other vertex. achieve this result applying 1-sum lemma for characteristic polynomial of graphs, neutrino identities relate entries eigenprojectors eigenvalues, variational principles eigenvalues (Cauchy interlacing the...

We introduce a subclass of linear recurrence sequences which we call poly-rational because they are denoted by rational expressions closed under sum and product. show that this class is robust giving several characterisations: polynomially ambiguous weighted automata, copyless cost-register formal series, whose eigenvalues roots numbers.

A classical result of Grothendieck and Lidskii says that the trace formula (that the trace of a nuclear operator is the sum of its eigenvalures provided the sequence of eigenvalues is absolutely summable) holds in Hilbert spaces. In 1988 Pisier proved that weak Hilbert spaces satisfy the trace formula. We exhibit a much larger class of Banach spaces, called Γ-spaces, that satisfy the trace form...