Mengxu Yuan

PhD Student | Department of Mathematics

Western University, CA

Hello!

I am a PhD student in the Department of Mathematics at the University of Western Ontario. My supervisor is Dr. Hristo Sendov. I completed my M.Sc. in Pure Mathematics at Western (2024-2025) under the supervision of Dr. Martin Pinsonnault, and my B.Sc. in Information and Computing Science at the School of Sciences (now the School of Mathematics and Statistics) at Wuhan University of Technology (2020-2024).

My research interests lie primarily in Matrix Analysis.

Outside of mathematics, I enjoy playing table tennis, badminton, and swimming.

You can find my CV here.

Contact

myuan89 [at] uwo [dot] ca

MC-102 | Middlesex College
Western University, CA

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Publications

Aggregate Bounds on the eigenvalues of the principal submatrices of a Hermitian matrix and majorization relations 2026
Hristo Sendov, Mengxu Yuan
Submitted , 18 pages

Few-shot Font Generation based on SAE and Diffusion Model 2024
Yizuo Shi, Wenxia Yang, Mengxu Yuan, Zeping Yi
Highlights in Science, Engineering and Technology (Proc. AMMSAC 2024) , 107 , 613-627

Talks

Aggregate Bounds on the Eigenvalues of the Principal Submatrices of a Hermitian Matrix and Majorization Relations
February 6, 2026
MC 108, Middlesex College, UWO
[Slides]
▸ View Abstract
We extend bounds, proved by R.C. Thompson in 1966, on the sum of the $j$-th largest eigenvalues of the $(n-1) \times (n-1)$ principal matrices of an $n \times n$ Hermitian matrix. Our bounds are stronger than just summing up Thompson's bounds. We achieve the extensions as a corollary of a more general result giving bounds on the zeros of the generalized derivatives of polynomials with real roots. We use the extended bounds to obtain majorization relationships between the eigenvalues of all $m \times m$ principal matrices of an $n \times n$ Hermitian matrix. These majorization relationships imply both a well-known majorization result by Schur and the well-known Szasz's inequalities. This talk is based on the preprint of the same title (arXiv:2601.16320). The presentation will primarily focus on Sections 1 and 2, covering the main results on aggregate bounds and their derivation.

Honors & Awards

  • Western Graduate Research Scholarship (WGRS) Sept. 2024 -- Present
    Western University
  • Graduate Fellowship Sept. 2024 -- Present
    Western University
  • Merit Student Nov. 2023
    Wuhan University of Technology
  • Third-Class Scholarship Nov. 2023
    Wuhan University of Technology
  • Second-Class Scholarship Nov. 2022
    Wuhan University of Technology
  • Third Prize, 14th 'Huazhong Cup' Mathematical Modeling Competition Jun. 2022
    Hubei Society for Industrial and Applied Mathematics
  • First Prize, 13th National College Student Mathematics Competition Dec. 2021
    The Chinese Mathematical Society
  • National Endeavor Scholarship Nov. 2021
    Wuhan University of Technology
  • Merit Student Nov. 2021
    Wuhan University of Technology

Teaching

Current Semester (Winter 2026)

Graduate Teaching Assistant for:

  • MATH 1225 (Methods of Calculus)
  • AM 1201 (Calculus & Probability with Biological Applications)

Past Semesters

Graduate Teaching Assistant for:

  • Fall 2025
    • MATH 2155 (Mathematical Structures)
    • MATH 2151 (Discrete Math for Engineers)
  • Summer 2025
    • MATH 1229 (Methods of Matrix Algebra)
    • MATH 1228 (Methods of Finite Mathematics)
  • Winter 2025
    • MATH 2700 (Linear Algebra II)
  • Fall 2024
    • CALC 1000 (Calculus I)

Learning Resources