On computing of arbitrary positive integer powers for one type of odd order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis. II. (English) Zbl 1113.65307
Summary: This paper is an extension of Part I [ibid. 183, No. 2, 1378–1380 (2006; Zbl 1106.65312)], in which the general expression of the lth power \((l\in \mathbb N)\) for one type of tridiagonal matrices of order \(n = 2p + 1\) \((p\in \mathbb N)\) is given. In this second part, we present the complete derivation of this general expression. Expressions of eigenvectors and Jordan’s form of the matrix and of the transforming matrix and its inverse are given, too.
MSC:
| 65F30 | Other matrix algorithms (MSC2010) |
| 15A21 | Canonical forms, reductions, classification |
| 15B57 | Hermitian, skew-Hermitian, and related matrices |
| 65F50 | Computational methods for sparse matrices |
Citations:
Zbl 1106.65312References:
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| [3] | J. Rimas, On computing of arbitrary positive integer powers for one type of odd order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis-I, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.05.144.; J. Rimas, On computing of arbitrary positive integer powers for one type of odd order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis-I, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.05.144. · Zbl 1106.65312 |
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