Article ID Journal Published Year Pages File Type
4598430 Linear Algebra and its Applications 2017 12 Pages PDF
Abstract

The energy of a symmetric matrix is the sum of the absolute values of its eigenvalues. We introduce a lower bound for the energy of a symmetric matrix partitioned into blocks. This bound is related to the spectrum of its quotient matrix. Furthermore, we study necessary conditions for the equality. Applications to the energy of the generalized composition of a family of arbitrary graphs are obtained. A lower bound for the energy of a graph with a bridge is given. Some computational experiments are presented in order to show that, in some cases, the obtained lower bound is incomparable with the well known lower bound 2m, where m is the number of edges of the graph.

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Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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