Bhatia, Rejendra ; Elsner, Ludwig
(1993)
*The q-binomial theorem and spectral symmetry*
Indagationes Mathematicae, 4
(1).
pp. 11-16.
ISSN 0019-3577

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0019-3577(93)90047-3

## Abstract

In various contexts, several mathematicians have discovered a binomial theorem of the following form: Let T_{1},T_{2} be complex matrices such that T_{2}T_{1} = qT_{1}T_{2}. Then (T_{1} + T_{2})^{n} = Σ(_{k = 0})^{n} α_{n,k}(q)T_{1}(k)T_{2}^{n-k} and the polynomials α_{n,k}(q) are given explicitly. We describe an application of this result in our work on matrices whose eigenvalues have certain symmetries.

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ID Code: | 97461 |

Deposited On: | 11 Feb 2013 06:07 |

Last Modified: | 11 Feb 2013 06:07 |

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