Relationship between the Inverses of a Matrix and a Submatrix

Authors

  • E. Juárez Ruiz Benemérita Universidad Autónoma de Puebla
  • R. Cortes Maldonado Benemérita Universidad Autónoma de Puebla
  • F. Pérez Rodríguez Benemérita Universidad Autónoma de Puebla

DOI:

https://doi.org/10.13053/cys-20-2-2083

Keywords:

Matrix inverse, submatrix, discrete Fourier transform

Abstract

A simple and straightforward formula for computing the inverse of a submatrix in terms of the inverse of the original matrix is derived. General formulas for the inverse of submatrices of order 𝑛 − 𝑘 as well as block submatrices are derived. The number of additions (or subtractions) and multiplications (or divisions) on the formula is calculated. A variety of numerical results are shown. 

Author Biographies

E. Juárez Ruiz, Benemérita Universidad Autónoma de Puebla

E. Juárez Ruiz has a Ph.D. degree in Mathematics from Benemérita Universidad Autónoma de Puebla. She works as a Research Professor at the Faculty of Electronics in the same university. Her research interests include applied mathematics and educational models mediated by Information and Communications Technologies (ICT). 

R. Cortes Maldonado, Benemérita Universidad Autónoma de Puebla

R. Cortés Maldonado has a B.Sc. degree in Electronics and an M.Sc. degree in Physics from Benemérita Universidad Autónoma de Puebla. Currently, he works on his Ph.D. research project on magnetic properties of superconductors. 

F. Pérez Rodríguez, Benemérita Universidad Autónoma de Puebla

F. Pérez Rodríguez has a Ph.D. degree in Physics and Mathematics from Kharkov State University. He is a National Investigator, Level 3. He is interested in optical and acoustical properties of solids, in metamaterials, and in superconductivity.

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Published

2016-06-25

Issue

Vol. 20 No. 2 (2016): 20-2 (2016)

Section

Articles

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