Abstract
The Fibonacci matrix [1, 1; 1, 0] is well known in the wide theme of Fibonacci numbers and their applications in various fields of mathematics, computer technologies and informatics, economics and biology. The article describes results of generalizations of the Fibonacci (2*2)-matrix on the basis of the tensor (Kronecker) product of matrices and also some features of Fibonacci-like (2n*2n)-matrices received in the result of such generalization. The main property of these considered matrices is that their exponentiation in integer powers k generates matrices, all entries of which are Fibonacci numbers with the same common factor 2 k−1.
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