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 descr ...

, 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 (mathematics), scalar-valued function (mathematics), function of the entries of a square matrix. The determinant of a matrix is commonly denoted , , or . Its value characterizes some properties of the ...

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

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

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

References

* Invariant theory {{math-stub