Alternant matrix

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" matrix may be written out as

:or more succinctly:$M\_\{i,j\}\; =\; f\_j(alpha\_i)$for all indices "i" and "j". (Some authors use the transpose of the above matrix.)

Examples of alternant matrices include Vandermonde matrices, for which $f\_i(alpha)=alpha^\{i-1\}$ and Moore matrices for which $f\_i(alpha)=alpha^\{q^\{i-1$.

Alternant matrices are used in coding theory in the construction of alternant codes.

ee also

* List of matrices

References

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