Generalized Matrix Multiplication and Its Some Applications

osman Kecilioglu

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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.


Generalized matrix multiplication, eigenvalue, eigenvector


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ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)