GENERALIZED MATRIX MULTIPLICATION AND ITS SOME APPLICATION

Osman Keçilioğlu, Halit Gündoğan

DOI Number
10.22190/FUMI1705789K
First page
789
Last page
798

Abstract


In this paper, generalized matrix multiplication is defined in R^{m,n}×R^{n,p} by using any scalar product in Rⁿ, where R^{m,n} denotes set of matrices of m rows and n columns. With this multiplication it has been shown that R^{n,n} is an algebra with unit. By considering this new multiplication we define eigenvalues and eigenvectors of square n×n matrix A. A special case is considered and generalized diagonalization is also introduced.

Keywords

Generalized matrix multiplication; inner product; eigenvector; eigenvalue.

Keywords


Generalized matrix multiplication, eigenvalue, eigenvector

Full Text:

PDF

References


A. A. Ergin: On the 1-parameter Lorentzian motions. Comm. Fac. Sci. Univ. Ankara Ser. A1 Math. Statist. 40 (1991), 59-66.

H. Gundogan and O. Kecilioglu: Lorentzian matrix multiplication and the motions on Lorentzian plane. Glas. Mat. Ser. III 41(61), no. 2 (2006), 329-334.

H. Gundogan and O. Kecilioglu: Pseudo Matrix Multiplication. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 66, no. 2, (2017), 37-43.

S. Lang: Linear Algebra. Addison-Wesley Publishing Co., London, 1971.

B. O'Neill: Semi-Riemannian Geometry With Applications to Relativity.Semi-Riemannian Geometry With Applications to Relativity", Academic Press, New York, 1983.




DOI: https://doi.org/10.22190/FUMI1705789K

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)