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Invariant functions of the elements of the powers of a square matrix

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
55
Identifiers
DOI: 10.1016/0024-3795(83)90172-6

Abstract

Abstract A square matrix A is raised to any real power n, negative or fractional values being permitted when A n can be defined; C is a matrix that commute with A. Linear identities existing between the elements of A n or C are investigated, in such a way that the number of elements in each identity is minimized in general. Both this number and the method of investigation depend on the Jordan canonical form of A, but if A has a special property, some of these identities and their method of derivation are independent of the Jordan canonical form.

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