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
are functions from a set
to a field
, and
, then the alternant matrix has size
and is defined by

or, more compactly,
. (Some authors use the transpose of the above matrix.) Examples of alternant matrices include Vandermonde matrices, for which
, and Moore matrices, for which
.
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