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In linear algebra, a tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the subdiagonal/lower diagonal, and the supradiagonal/upper diagonal. For example, the following matrix is tridiagonal:
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In mathematics, in particular linear algebra, the Bunch–Nielsen–Sorensen formula, named after James R. Bunch, Christopher P. Nielsen and Danny C. Sorensen, expresses the eigenvectors of the sum of a symmetric matrix and the outer product, , of vector with itself.
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A Bohemian matrix family is a set of matrices whose free entries come from a single discrete, usually finite population, denoted by the matrix list P. Each input of any matrix from this particular Bohemian matrix family is required to be an element of the set P. Such matrices containing these properties are defined as Bohemian matrices. Bohemian matrices may possess additional structure, a Toeplitz matrix or an upper Hessenberg matrix, for example. Usually only one Bohemian matrix family with a fixed population P is studied at a time, so one can classify any given matrix as being Bohemian or not without significant ambiguity.
References
- ↑ Beresford Neill Parlett at the Mathematics Genealogy Project
- ↑ "Beresford N. Parlett". Mathematics Department, U. C. Berkeley.
- 1 2 Bunch, James R. (1995). "Editorial (introducing special issue dedicated to Beresford Parlett and William Kahan on their 60th birthdays)". Numerical Linear Algebra with Applications. 2 (2): 85. doi:10.1002/nla.1680020202. (See William Kahan.)
- ↑ "Prize History". SIAM Activity Group on Linear Algebra Best Paper Prize, SIAM.
- 1 2 "Beresford N. Parlett". Electrical Engineering and Computer Sciences, U. C. Berkeley.
- ↑ Hirsch, Morris W.; Palais, Richard S. (1992). "Editors' remarks (on two complexity theory surveys in the Bulletin)". Bulletin of the American Mathematical Society. New Series. 26: 1–2. arXiv: math/9201262 . doi:10.1090/S0273-0979-1992-00238-0.
- ↑ Stewart, G. W. (1981). "Book Review: The symmetric eigenvalue problem". Bulletin of the American Mathematical Society. 4 (3): 368–374. doi: 10.1090/s0273-0979-1981-14918-1 .
