Kecilioglu, OsmanGundogan, Halit2025-01-212025-01-2120170352-96652406-047Xhttps://doi.org/10.22190/FUMI1705789Khttps://hdl.handle.net/20.500.12587/24859In this paper, a generalized matrix multiplication is defined in R-m,R-n x R-n,R-p by using any scalar product in R-n, where R-m,R-n denotes set of matrices of m rows and n columns. With this multiplication it has been shown that R-n,R-n is an algebra with unit. By considering this new multiplication we define eigenvalues and eigenvectors of square n x n matrix A. A special case is considered and generalized diagonalization is also introduced.eninfo:eu-repo/semantics/closedAccessGeneralized matrix multiplication; inner product; eigenvector; eigenvalueArticle32578979810.22190/FUMI1705789KWOS:000424465300013N/A