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 In mathematical invariant theory, the catalecticant of a form of even degree is a polynomial in its coefficients that vanishes when the form is a sum of an unusually small number of powers of linear forms. It was introduced by ; see . The word c ...

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 and ...

of the ''n'' by ''n''

Hankel matrix In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a square matrix in which each ascending skew-diagonal from left to right is constant, e.g.: \qquad\begin a & b & c & d & e \\ b & c & d & e & f \\ c & d & ...

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

References

* Invariant theory {{math-stub