Eckart-Young-Mirsky theorem:

Decomposition In Kronecker Products

Authors

Abstract

The objective of this Scientific Article is to present the decomposition into Kronecker products using the Singular Value Decomposition (SVD), as well as its relationship with the Eckart-Young-Mirsky Theorem. To this end, we carried out a literature search and demonstrated the main properties of SVD and Kronecker's product. Furthermore, we use other methods for decomposition, such as the power method and Householder reflections in order to obtain the QR decomposition of symmetric matrices.

Author Biographies

  • Tomy Felixon, UNICAMP/IMECC

    He has a bachelor's degree and a degree in mathematics from the State University of Campinas (2019) and (2020), respectively, and a specialization in Didactic-Pedagogical Training for Distance Learning Courses and in Teaching for Professional and Technological Education from the Virtual University of State of São Paulo (2022) and the Federal Institute Espírito Santo (2023), respectively. He has a master's degree in Applied Mathematics from the State University of Campinas (2023). He is currently a PhD student in Applied Mathematics at the same university. He worked as a facilitator at the Virtual University of the State of São Paulo from August 2020 to July 2022.

  • Fabiana Correia Pereira, UNICAMP/IMECC

    Graduated in Mathematics from the Federal Institute of Science, Education and Technology of Maranhão (2012). Specialist in Statistics from the State University of Maranhão - UEMA (2018). Specialist in Public Management from the Federal University of Maranhão - UFMA (2016). Professional Master's Degree in Applied and Computational Mathematics from the State University of Campinas - UNICAMP (2022). She is currently a Technician in Educational Affairs at the Federal University of Maranhão-UFMA.

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Published

2024-12-31

Issue

Vol. 11 No. 2 (2023): Matemática e Estatística em Foco

Section

Matemática Aplicada