Counting \(d\)-dimensional hyperinvariant subspaces of a Weyr matrix. (English) Zbl 1329.15008
Summary: A characterization of hyperinvariant subspaces is given in terms of Weyr characteristic. Using this characterization we compute the number of the \(d\)-dimensional hyperinvariant subspaces.
MSC:
| 15A03 | Vector spaces, linear dependence, rank, lineability |
| 15B99 | Special matrices |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
References:
| [1] | Astuti, P.; Wimmer, H. K., Hyperinvariant, characteristic and marked subspaces, Oper. Matrices, 3, 261-270 (2009) · Zbl 1181.15009 |
| [2] | Bhavanari, S.; Prasad, S., Discrete Mathematics and Graph Theory (2009), Eastern Economy Edition |
| [3] | Fillmore, P. A.; Herrero, D. A.; Longstaff, W. E., The hyperinvariant subspace lattice of a linear transformation, Linear Algebra Appl., 17, 125-132 (1977) · Zbl 0359.47005 |
| [4] | Gohberg, I.; Lancaster, P.; Rodman, L., Invariant Subspaces of Matrices with Applications (1986), SIAM · Zbl 0608.15004 |
| [5] | O’Meara, K. C.; Clark, J.; Vinsonhaler, C. I., Advanced Topics in Linear Algebra: Weaving Matrix Problems Through the Weyr Form (2011), Oxford University Press: Oxford University Press Oxford · Zbl 1235.15013 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
