二次变换与矩阵双正交多项式：一种$\mathcal{LU}$分解方法
Quadratic transformation and matrix biorthogonal polynomials: an $\mathcal{LU}$ factorization approach
摘要：
本文给出了当Gram矩阵中所有偶数元均为零时矩阵双正交多项式的$LU$方法。这在简要讨论的二次变换的情况下出现。此外，主对角线的革兰氏矩阵是零对角线，我们提出的理论，从这一事实。准确地说，我们讨论了Christoffel变换和核多项式的矩阵表示，通常称为ABC定理。最后，我们提供了一个例子，我们的结果假设革兰氏矩阵具有汉克尔对称性。
英文摘要：
The manuscript presents the $LU$ approach to matrix biorthogonal polynomials when all the even ordered entries in the Gram matrix are zero. This arises in case of a quadratic transformation which is briefly discussed. Further, the main diagonal of the Gram matrix is a zero diagonal and we present the theory that follows from this fact. Precisely, we discuss the Christoffel transformation and matrix representations of the kernel polynomials, usually called the ABC Theorem. Finally, we provide an illustration of our results assuming the Gram matrix has Hankel symmetry.
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