Mth Power of an N × N Matrix and Its Connection with the Generalized Lucas Polynomials
- 1 August 1969
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 10 (8) , 1474-1476
- https://doi.org/10.1063/1.1664992
Abstract
The Mth power of an N × N matrix is expressed via the Cayley‐Hamilton theorem as a linear combination of the lower powers of the matrix. The polynomial coefficients of the lower powers of the matrix are expressed in terms of polynomials in N variables, termed the generalized Lucas polynomials. The independent variables in the generalized Lucas polynomials are the traces of the lower powers of the matrix.Keywords
This publication has 4 references indexed in Scilit:
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- The Matrix Operator ex and the Lucas PolynomialsJournal of Mathematics and Physics, 1964
- An Application of ContinuantsMathematics Magazine, 1964
- An Application of ContinuantsMathematics Magazine, 1964