Zhekai Pang

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math.RA2026

A sharp weighted commutator inequality for rank-one matrices

Zhekai Pang

Let $A \in C^{n \times n}$ be positive definite Hermitian, where $n \geq 2$ , and define $∥ X ∥_{A}^{2} = tr (A X^{*} X)$ for all $X \in C^{n \times n}$ . We determine the sm…

math.RA2026

Counterexamples to a multivariable matrix Young conjecture

Zhekai Pang

We disprove Conjecture 5.1 of Lin concerning a multivariable extension of Ando's matrix Young inequality for positive semidefinite matrices. For every integer $m \geq 4$ , the conject…

math.RA2026

Proof of Dittert's conjecture for dimensions \texorpdfstring{$n\ge 17$}{n >= 17}

Zhekai Pang

Dittert's conjecture gives a sharp upper bound for the Dittert functional on nonnegative matrices whose entries sum to $n$. It extends the van der Waerden permanent problem from…

math.RA2026

Real Matrices as Linear Combinations of Three Orthogonal Matrices

Zhekai Pang

Li and Poon proved that every real square matrix is a real linear combination of four real orthogonal matrices. The resulting question, recorded by Zhan, asks whether four terms ar…

A sharp weighted commutator inequality for rank-one matrices

Counterexamples to a multivariable matrix Young conjecture

Proof of Dittert's conjecture for dimensions \texorpdfstring{\(n\ge 17\)}{n >= 17}

Real Matrices as Linear Combinations of Three Orthogonal Matrices