Block Matrices in Linear Algebra
PRIMUS Problems, Resources, and Issues in Mathematics Undergraduate Studies ISSN: 1051-1970 (Print) 1935-4053 (Online) Journal homepage: https://www.tandfonline.com/loi/upri20 Block Matrices in Linear Algebra Stephan Ramon Garcia & Roger A. Horn To cite this article: Stephan Ramon Garcia & Roger A. Horn (2020) Block Matrices in Linear Algebra, PRIMUS, 30:3, 285-306, DOI: 10.1080/10511970.2019.1567214 To link to this article: https://doi.org/10.1080/10511970.2019.1567214 Accepted author version posted online: 05 Feb 2019. Published online: 13 May 2019. Submit your article to this journal Article views: 86 View related articles View Crossmark data Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=upri20 PRIMUS, 30(3): 285–306, 2020 Copyright # Taylor & Francis Group, LLC ISSN: 1051-1970 print / 1935-4053 online DOI: 10.1080/10511970.2019.1567214 Block Matrices in Linear Algebra Stephan Ramon Garcia and Roger A. Horn Abstract: Linear algebra is best done with block matrices. As evidence in sup- port of this thesis, we present numerous examples suitable for classroom presentation. Keywords: Matrix, matrix multiplication, block matrix, Kronecker product, rank, eigenvalues 1. INTRODUCTION This paper is addressed to instructors of a first course in linear algebra, who need not be specialists in the field. We aim to convince the reader that linear algebra is best done with block matrices. In particular, flexible thinking about the process of matrix multiplication can reveal concise proofs of important theorems and expose new results. Viewing linear algebra from a block-matrix perspective gives an instructor access to use- ful techniques, exercises, and examples.
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