Alternant matrix

In linear algebra, an alternant matrix is a matrix formed by applying a finite list of functions pointwise to a fixed column of inputs. An alternant determinant is the determinant of a square alternant matrix. 
Generally, if formula_1 are functions from a set formula_2 to a field formula_3, and formula_4, then the alternant matrix has size formula_5 and is defined by
or, more compactly, formula_7. (Some authors use the transpose of the above matrix.) Examples of alternant matrices include Vandermonde matrices, for which formula_8, and Moore matrices, for which formula_9.