Explanipedia

Revisiting a sharpened version of Hadamard's determinant inequality Open

Minghua Lin, Gord Sinnamon · 2020

An extension of Harnack type determinantal inequality Open

Minghua Lin, Fuzhen Zhang · 2017

We revisit and comment on the Harnack type determinantal inequality for contractive matrices obtained by Tung in the nineteen sixtieth and give an extension of the inequality involving multiple positive semidefinite matrices.

Power majorization between the roots of two polynomials Open

Minghua Lin, Gord Sinnamon · 2016

It is shown that if two hyperbolic polynomials have a particular factorization into quadratics, then their roots satisfy a power majorization relation whenever key coefficients in their factorizations satisfy a corresponding majorization r…

New properties for certain positive semidefinite matrices Open

Minghua Lin · 2016

We bring in some new notions associated with $2\times 2$ block positive semidefinite matrices. These notions concern the inequalities between the singular values of the off diagonal blocks and the eigenvalues of the arithmetic mean or geom…

On a determinantal inequality arising from diffusion tensor imaging Open

Minghua Lin · 2016

In comparing geodesics induced by different metrics, Audenaert formulated the following determinantal inequality $$\det(A^2+|BA|)\le \det(A^2+AB),$$ where $A, B$ are $n\times n$ positive semidefinite matrices. We complement his result by p…

A Singular Value Inequality Related to a Linear Map Open

Minghua Lin · 2016

If $\begin{bmatrix}A & X \\ X^* & B\end{bmatrix}$ is positive semidefinite with each block $n\times n$, we prove that $$2s_j\Big(\Phi(X)\Big)\le s_j\Big(\Phi(A+B)\Big), \qquad j=1, \ldots, n,$$ where $\Phi: X\mapsto X+(\tr X)I$ and $s_j(\c…

Bilinear characterizations of companion matrices Open

Minghua Lin, Hȧrald K. Wimmer · 2016

Companion matrices of the second type are characterized by properties that involve bilinear maps.

On Drury's solution of Bhatia \& Kittaneh's question Open

Minghua Lin · 2016

Let $A, B$ be $n\times n$ positive semidefinite matrices. Bhatia and Kittaneh asked whether it is true $$ \sqrt{σ_j(AB)}\le \frac{1}{2} λ_j(A+B), \qquad j=1, \ldots, n$$ where $σ_j(\cdot)$, $λ_j(\cdot)$, are the $j$-th largest singular val…

Some inequalities for sector matrices Open

Minghua Lin · 2016

Two new inequalities are proved for sector matrices.The first one complements a recent result in [Oper.Matrices, 8 (2014Matrices, 8 ( ) 1143Matrices, 8 ( -1148]]; the second one is an analogue of the AM-GM inequality, where the geometric m…

Determinantal inequalities for block triangular matrices Open

Minghua Lin · 2015

be an n -square matrix, where X,Z are r -square and (nr) -square, respectively.Among other determinantal inequalities, it is proved thatwith equality if and only if Y = 0 .

Inequalities related to 2 ✕ 2 block PPT matrices Open

Minghua Lin · 2015

of matrices.Among others, we show that the Hua matrix, which is PPT, reveals a remarkable singular value inequality for contractive matrices.

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