Abstract
In this note, we first prove an inequality for sector matrices. This complements a result due to Kittaneh and Sakkijha (Linear Multilinear Algebra, 2018, https://doi.org/10.1080/03081087.2018.1441800) concerning accretive–dissipative matrices. And then we present two singular value inequalities for sector matrices which are similar to Yang and Lu’s inequalities (J. Inequal. Appl. 2018:183, 2018).
Highlights
We present two singular value inequalities for sector matrices which are similar to Yang and Lu’s inequalities
We denote by Mn(C) the set of n × n complex matrices
A matrix whose numerical range is contained in a sector region Sα is called a sector matrix [10]
Summary
We denote by Mn(C) the set of n × n complex matrices. For A ∈ Mn(C), the conjugate transpose of. Are called the real part and imaginary part of A, respectively Recall that a norm · on Mn(C) is unitarily invariant if UAV = A for any A ∈ Mn(C) and unitarily matrices U, V ∈ Mn(C). For p ≥ 1, the Schatten p-norm of A ∈ Mn(C) is defined as A p = (
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