In mathematical

invariant theory Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit descri ...

, the canonizant or canonisant is a covariant of forms related to a canonical form for them.

Canonizants of a binary form

The canonizant of a binary form of degree 2''n'' – 1 is a covariant of degree ''n'' and order ''n'', given by the catalecticant of the penultimate emanant, which is the

determinant In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if ...

of the ''n'' by ''n'' Hankel matrix with entries ''a''_''i''+''j''''x'' + ''a''_{''i''+''j''+1}''y'' for 0 ≤ ''i'',''j'' < ''n''.

References

* Invariant theory {{math-stub