Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Matrix Algebra, Basics of

  • Ayman Badawi
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_151



Augmented matrix

An augmented matrix of a system of linear equations written in matrix form CX = B is a matrix of the form [C|B], where C is the coefficient matrix of the system and B is the constant column of the system

Consistent and inconsistent system of linear equations

A system of linear equations is said to be consistent if it has a solution, and it is called inconsistent if it has no solutions

Cramer rule

Cramer’s rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of...

This is a preview of subscription content, log in to check access.


  1. Axler S (1997) Linear algebra done right. Springer, BerlinzbMATHCrossRefGoogle Scholar
  2. Beezer RA (2012) A first course in linear algebra. Congruent Press, TacomaGoogle Scholar
  3. Bernstein DS (2005) Matrix mathematics: theory, facts, and formulas with application to linear systems theory. Princeton University Press, PrincetonzbMATHGoogle Scholar
  4. Blyth TS, Robertson EF (2002) Basic linear algebra. Springer, BerlinzbMATHCrossRefGoogle Scholar
  5. Kaw A (2011) Introduction to matrix algebra, 2nd edn. University of South Florida, TampaGoogle Scholar
  6. Lang S (1986) Introduction to linear algebra. Springer, BerlinzbMATHCrossRefGoogle Scholar
  7. Lay DC (2003) Linear algebra and its applications, 3rd edn. Pearson, TorontoGoogle Scholar
  8. Robbiano L (2011) Linear algebra for everyone. Springer, BerlinzbMATHGoogle Scholar
  9. Shores TS (2007) Applied linear algebra and matrix analysis. Springer, BerlinzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsAmerican University of SharjahSharjahUAE

Section editors and affiliations

  • Suheil Khoury
    • 1
  1. 1.American University of SharjahSharjahUnited Arab Emirates