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Does the following matrix have a specific name?

$$A(a,r)=\begin{bmatrix} 1 & a & a^2 & a^3 \\ 0 & r & 2ar & 3a^2r \\ 0 & 0 & r^2 & 3ar^2 \\ 0 & 0 & 0 & r^3 \end{bmatrix} $$

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    $\begingroup$ Italian wikipedia calls them Pascal matrices, but it appears that in English and French literature Pascal matrices are only your $A(1,1)$. $\endgroup$ Jul 28, 2022 at 9:43
  • $\begingroup$ In the examples in the italian page, when mentioning about the group $T(h,d)$ it also shows the relation with a Vandermonde vector. Do you know if a Vandermonde vector remains still a Vandermonde vector IFF the transformation is Pascal? $\endgroup$
    – yes
    Jul 29, 2022 at 9:33
  • $\begingroup$ No, I do not know. $\endgroup$ Jul 29, 2022 at 22:19

1 Answer 1

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Upper Pascal Matrix (generalized) seems to fit the description.

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  • $\begingroup$ Do you know if a Vandermonde vector remains still a Vandermonde vector IFF the transformation is Pascal? $\endgroup$
    – yes
    Aug 1, 2022 at 7:09

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