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• W1613737551 abstract "Let $K$ denote a field, and let $V$ denote a vector space over $K$ with finite positive dimension. Consider a pair of linear transformations $A:Vto V$ and $A^*:Vto V$ that satisfy both conditions below: (i) There exists a basis for $V$ with respect to which the matrix representing $A$ is diagonal, and the matrix representing $A^*$ is irreducible tridiagonal. (ii) There exists a basis for $V$ with respect to which the matrix representing $A^*$ is diagonal, and the matrix representing $A$ is irreducible tridiagonal. Such a pair is called a Leonard pair on $V$. In this paper we introduce a mild generalization of a Leonard pair called a tridiagonal pair. A Leonard pair is the same thing as a tridiagonal pair such that for each transformation all eigenspaces have dimension one." @default.
• W1613737551 created "2016-06-24" @default.
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• W1613737551 date "2004-06-27" @default.
• W1613737551 modified "2023-09-27" @default.
• W1613737551 title "Some algebra related to $P$-and $Q$-polynomial association schemes" @default.
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