Block Matrices in Linear Algebra

Abstract

Linear algebra is best done with block matrices. As evidence in support of this thesis, we present numerous examples suitable for classroom presentation.

Keywords:

• Matrix
• matrix multiplication
• block matrix
• Kronecker product
• rank
• eigenvalues

Additional information

Funding

Partially supported by National Science Foundation Grants DMS-1800123 and DMS-1265973, and David L. Hirsch III and Susan H. Hirsch Research Initiation Grant.

Notes on contributors

Stephan Ramon Garcia

Stephan Ramon Garcia is W.M. Keck Distinguished Service Professor and Professor of Mathematics at Pomona College. He is the author of four books and over eighty-five research articles in operator theory, complex analysis, matrix analysis, number theory, discrete geometry, and other fields. He is on the editorial boards of the Notices of the American Mathematical Society (2019–), Proceedings of the American Mathematical Society (2016–), Involve (2011–), and The American Mathematical Monthly (2017–). He received four NSF research grants as principal investigator and five teaching awards from three different institutions. He is a fellow of the American Mathematical Society (2019) and the inaugural recipient of the AMS Dolciani Prize for Excellence in Research.

Roger A. Horn

Roger A. Horn was Research Professor of Mathematics at the University of Utah. His publications include the Cambridge University Press books Matrix Analysis and Topics in Matrix Analysis as well as more than 100 research articles in matrix analysis, statistics, health services research, complex variables, probability, differential geometry, and analytic number theory. He was Editor of The American Mathematical Monthly (1996–2001), the MAA Spectrum book series (1992–1995), and the MAA Carus Mathematical Monographs (2002–2005). He has also served on the editorial boards of the SIAM Journal of Matrix Analysis, Linear Algebra and its Applications, and the Electronic Journal of Linear Algebra.