Revisiting Schurs bound on the largest singular value
نویسنده
چکیده
We give upper and lower bounds on the largest singular value of a matrix using analogues to walks in graphs. For nonnegative matrices these bounds are asymptotically tight. In particular, the following result improves a bound due to Schur. If A = (aij) is an m n complex matrix, its largest singular value satis es 2 (A) max i2[m] P j2[n] jaij j cj max aij 6=0 ricj ; where ri = P k2[n] jaikj ; cj = P k2[m] jakj j : Keywords: largest singular value, Schurs bound, singular values, walks. AMS classi cation: 15A42
منابع مشابه
Revisiting Schur ’ s bound on the largest singular value Vladimir Nikiforov
We give upper and lower bounds on the largest singular value of a matrix using analogues to walks in graphs. For nonnegative matrices these bounds are asymptotically tight. In particular, the following result improves a bound due to Schur. If A = (aij) is an m× n complex matrix, its largest singular value satisfies σ (A) ≤ max i∈[m] ∑ j∈[n] |aij| cj ≤ max aij 6=0 ricj, where ri = ∑ k∈[n] |aik| ...
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