A Specific Case of a Family of Symmetric Matrices That Are Simultaneously Diagonalizable via Congruence

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Published: Jun 20, 2025
Keywords:
constrained optimization, matrix transformations, quadratic forms, simultaneous diagonalization via congruence, symmetric matrices

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Vo Duc Tu Duy1,*,
1 Department of Research Administration and International Relations, University of Phan Thiet, Vietnam

Abstract

This paper establishes a new condition for a specific family of symmetric matrices to be simultaneously diagonalizable via congruence. The paper considers a structured family of symmetric matrices satisfying a particular rank condition, which ensures the existence of a nonsingular congruence transformation that simultaneously diagonalizes all the initial matrices. Explicit examples are provided to illustrate the sharpness of our condition. 

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How to Cite
Vo, D. T. D. (2025). A Specific Case of a Family of Symmetric Matrices That Are Simultaneously Diagonalizable via Congruence. The University of Phan Thiet Journal of Science, 3(2), 42-50. https://tapchikhoahocupt.vn/index.php/uptjs/article/view/68
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Vol. 3 No. 2 (2025): The University of Phan Thiet Journal of Science
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Articles

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