Another proof of a result on the doubly superstochastic matrices. (English) Zbl 1551.15030

Huang, Shaowu

Linear Multilinear Algebra 72, No. 11, 1761-1765 (2024).

Let \(H\in\mathbb{R}^{2n\times 2n}\) be symplectic, that is \[ H^TJH=J,\quad J=\left( \begin{array}{cc} 0&I_n\\ -I_n&0 \end{array} \right). \] The author establishes a trace inequality for \(H\) and, as a consequence, gives a new proof of a theorem by R. Bhatia and T. Jain [J. Math. Phys. 56: 112201 (2015; Zbl 1329.15048)] on a doubly superstochastic matrix

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•  Wikipedia
•  Wolfram MathWorld

corresponding to \(H\). An entrywise nonnegative square matrix \(U\) is doubly superstochastic if there is a doubly stochastic matrix

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•  Wolfram MathWorld

\(V\) such that \(U\ge V\) entrywise.

Reviewer: Jorma K. Merikoski (Tampere)

MSC:

15B51	Stochastic matrices
15A15	Determinants, permanents, traces, other special matrix functions
15A45	Miscellaneous inequalities involving matrices

Keywords:

symplectic matrix; trace; doubly superstochastic matrix

Citations:

Zbl 1329.15048

References:

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