Abstract
A feature of the computer solution of matrix problems is that often there is a problem of accumulation of rounding errors. This may lead to an incorrect result. J.H. Wilkinson developed efficient methods for finding eigenvalues and eigenvectors of matrices based on the well-known Francis-Kublanovska’s QR-algorithm. Now there are new problems of algebra, the methods of solution of which require further improvement. There is a problem of reducing a few initial matrices into a block-diagonal or block-triangular form. This requires the development of a new approaches to solving the problems of finding the centralizer of matrices and constructing an algebra with a unit generated by these matrices. For the first of these problems, it was possible to create an effective method. The next problem is to create an efficient algorithm for constructing the algebra generated by matrices
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