In linear algebra, an alternant matrix is a matrix with a particular structure, in which successive columns have a particular function applied to their entries. An alternant determinant is the determinant of an alternant matrix. Such a matrix of size m × n may be written out as
or more succinctly
for all indices i and j. (Some authors use the transpose of the above matrix.)
If and the functions are all polynomials, there are some additional results: if for any , then the determinant of any alternant matrix is zero (as a row is then repeated), thus divides the determinant for all . As such, if one takes
- Thomas Muir (1960). A treatise on the theory of determinants. Dover Publications. pp. 321–363.
- A. C. Aitken (1956). Determinants and Matrices. Oliver and Boyd Ltd. pp. 111–123.
- Richard P. Stanley (1999). Enumerative Combinatorics. Cambridge University Press. pp. 334–342.
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