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Lucas Numbers and Determinants
-
and
Published/Copyright:
January 24, 2012
Abstract.
In this article, we present two infinite dimensional matrices
whose entries are recursively defined, and show that the sequence
of their principal minors form the Lucas sequence, that is
Keywords.: Determinant; Principal Minor; Matrix
Factorization; Lucas Sequence; Nonhomogeneous Recurrence
Relation; Toeplitz Matrix
Received: 2010-04-04
Revised: 2011-05-09
Accepted: 2011-05-27
Published Online: 2012-01-24
Published in Print: 2012-February
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Prelims
- Selmer's Multiplicative Algorithm
- Lucas Numbers and Determinants
- A Combinatorial Proof of Guo's Multi-Generalization of Munarini's Identity
- Enumeration of Triangles in Quartic Residue Graphs
- A remark on the Boros–Moll Sequence
- A Relation Between Triangular Numbers and Prime Numbers
- Some Remarks on a Paper of V. A. Liskovets
- A Combinatorial Proof of a Recursive Formula for Multipartitions
- Aliquot Cycles of Repdigits
- Digital Sums and Functional Equations
Keywords for this article
Determinant;
Principal Minor;
Matrix
Factorization;
Lucas Sequence;
Nonhomogeneous Recurrence
Relation;
Toeplitz Matrix
Articles in the same Issue
- Prelims
- Selmer's Multiplicative Algorithm
- Lucas Numbers and Determinants
- A Combinatorial Proof of Guo's Multi-Generalization of Munarini's Identity
- Enumeration of Triangles in Quartic Residue Graphs
- A remark on the Boros–Moll Sequence
- A Relation Between Triangular Numbers and Prime Numbers
- Some Remarks on a Paper of V. A. Liskovets
- A Combinatorial Proof of a Recursive Formula for Multipartitions
- Aliquot Cycles of Repdigits
- Digital Sums and Functional Equations
