The Energy of Graphs and Matrices
نویسنده
چکیده
Given a complex m × n matrix A, we index its singular values as σ1 (A) ≥ σ2 (A) ≥ ... and call the value E (A) = σ1 (A)+σ2 (A)+ ... the energy of A, thereby extending the concept of graph energy, introduced by Gutman. Let 2 ≤ m ≤ n, A be an m×n nonnegative matrix with maximum entry α, and ‖A‖ 1 ≥ nα. Extending previous results of Koolen and Moulten for graphs, we prove that E (A) ≤ ‖A‖1 √ mn + √
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تاریخ انتشار 2006