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The CMV Matrix and the Generalized Lanczos Process
- Source :
- Journal of Mathematical Sciences. 232:837-843
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
Abstract
- The CMV matrix is the five-diagonal matrix that represents the operator of multiplication by the independent variable in a special basis formed of Laurent polynomials orthogonal on the unit circle C. The article by Cantero, Moral, and Velazquez, published in 2003 and describing this matrix, has attracted much attention because it implies that the conventional orthogonal polynomials on C can be interpreted as the characteristic polynomials of the leading principal submatrices of a certain five-diagonal matrix. The present paper recalls that finite-dimensional sections of the CMV matrix appeared in papers on the unitary eigenvalue problem long before the article by Cantero et al. was published. Moreover, band forms were also found for a number of other situations in the normal eigenvalue problem.
- Subjects :
- Statistics and Probability
Pure mathematics
Basis (linear algebra)
Applied Mathematics
General Mathematics
Operator (physics)
010102 general mathematics
Block matrix
010103 numerical & computational mathematics
Mathematics::Spectral Theory
01 natural sciences
Matrix (mathematics)
Unit circle
Orthogonal polynomials
Multiplication
0101 mathematics
Eigenvalues and eigenvectors
Mathematics
Subjects
Details
- ISSN :
- 15738795 and 10723374
- Volume :
- 232
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Sciences
- Accession number :
- edsair.doi...........6cf734fada3d2a6f1ec56c1b949b900d