Commit 2025-03-05 20:21 b8853be2

feat(Vandermonde): vandermonde matrices with exceptional rows (#22377) A Vandermonde matrix is usually taken to have rows of the form [1, a, a^2, ... a^(n-1)], but it is also in some contexts mathematically meaningful to 'projectively' generalize to rows of the form [b^(n-1),a * b^(n-2), ..., a^(n-1)]. Up to scalings, this is effectively just allowing new rows parallel to [0, ..., 0, 1]. We define a new type of matrix rectVandermonde allowing for rows of this generalized form with an arbitrary indexing type for the rows, and projVandermonde, which is the square matrix version that directly generalizes vandermonde. We also prove a formula for their determinant, and derive the proof of det_vandermonde as a special case.