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We consider a pair of diagonalizable matrices $A,A^*$ in $\\text{Mat}_{d+1}(\\mathbb{F})$, each acts in an irreducible tridiagonal fashion on an eigenbasis for the other one. Such a pair is called a Leonard pair in $\\text{Mat}_{d+1}(\\mathbb{F})$. For a Leonard pair $A,A^*$ there is a nonzero scalar $q$ that is used to describe the eigenvalues of $A$ and $A^*$. 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Let $\\text{Mat}_{d+1}(\\mathbb{F})$ denote the $\\mathbb{F}$-algebra consisting of the $(d+1) \\times (d+1)$ matrices that have all entries in $\\mathbb{F}$. We consider a pair of diagonalizable matrices $A,A^*$ in $\\text{Mat}_{d+1}(\\mathbb{F})$, each acts in an irreducible tridiagonal fashion on an eigenbasis for the other one. Such a pair is called a Leonard pair in $\\text{Mat}_{d+1}(\\mathbb{F})$. For a Leonard pair $A,A^*$ there is a nonzero scalar $q$ that is used to describe the eigenvalues of $A$ and $A^*$. 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