Examining Possible LU Decompositions

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Published: Jun 16, 2021
Keywords:
GeoGebra, linear algebra, LU decomposition

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Ly Jacky Nhiayi
Cal State Los Angeles
Tuyetdong Phan-Yamada
CSU Los Angeles

Abstract

LU decomposition is a fundamental in linear algebra. Numerous tools exists that provide this important factorization. The authors present the conditions for a matrix to have none, one, or infinitely many LU factorizations. In the case where no factorization exists, the authors illustrate how to approximate an LU decomposition by considering LU factorization of nearby matrices.

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Vol. 9 No. 1: North American GeoGebra Journal
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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Author Biographies

Ly Jacky Nhiayi, Cal State Los Angeles

Ly Jacky Nhiayi is an undergraduate computer science major at California State University---Los Angeles. Jacky enjoys studying real-world applications, number theory, and graph theory.

Tuyetdong Phan-Yamada, CSU Los Angeles

Tuyetdong Phan-Yamada is a lecturer at the Department of Mathematics, CSU Los Angeles.  She earned her Bachelor degree from UC Irvine and Master degree from CSU Los Angeles.  She enjoys building interactive graphical illustrations with GeoGebra, which she integrates into her lesson plans in Trigonometry, Geometry, Statistics, Calculus, and other courses. She has presented much of this work in conference and in journals. Her paper, "Hypocycloids and Hypotrochoids" was on the front page of MathAMATYC Educator Journal on September 2014. She extended her computational activities from the classroom to industry practice as a Summer' 14 faculty research fellow at JPL, Pasadena. She is also a board member of CMC3-South Spring Annual Conference.