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For nonnegative matrices A =( aij) ∈ Rn×m , B =( bij) ∈ Rm×n and any t ∈ (0,1), we present σ(St(A,B)) σ(A)tσ(B)1−t ,i n whichSt(A,B )=( atijb 1−t ji ) and σ(·) denotes the largest singular value. Using the result obtained, the inequality... more
For nonnegative matrices A =( aij) ∈ Rn×m , B =( bij) ∈ Rm×n and any t ∈ (0,1), we present σ(St(A,B)) σ(A)tσ(B)1−t ,i n whichSt(A,B )=( atijb 1−t ji ) and σ(·) denotes the largest singular value. Using the result obtained, the inequality σ(A ◦B) σ(A ◦ A)σ(B ◦ B) for matrices A =( aij) and B =( bij) ∈ Cn×m is established. Here, A ◦ B =( aijbij) ,a nd¯ bij denotes the complex conjugate of bij . Finally, some inequalities for the spectral radius are also studied.
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... ρ(Bij) = ||Bij||2 ⩾ ||Fij||2. Let A = (aij) ∈ Rn×n be a nonnegative matrix, and let S(A)=(sij) be the geo-metric symmetrization of A with sij = (aijaji) 1 2 . Schwenk [11] showed that ρ(A) ⩾ ρ(S(A)), which, together with Theorems 1 ...
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ABSTRACT