JP Journal of Algebra, Number Theory and Applications
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Abstract: It is well known that the
usual algorithms for Jordan canonical form and Jordan bases are very
complicated. In this paper, using the basic information which is easily to be
obtained, i.e., the eigenvalue andits algebraic multiplicity we defined the generalized matrices of A, which
convert the problem of Jordan canonical form and Jordan bases into that of
generalized eigenmatrices. We obtained a system of linear equations with
generalized Vandermond matrix being its coefficient matrix, through solving
which we can get all generalized eigenmatrices. In dealing with matrix functions
and their integrals, it will simplify the computation to replace Jordan
canonical form and Jordan bases by generalized eigenmatrices.
Keywords and phrases: Jordan canonical form, characteristic polynomial, generalized eigenmatrix, matrix function, linear system.
