Gerbaldi's theorem
Encyclopedia
In linear algebra
and projective geometry
, Gerbaldi's theorem, proved by , states that one can find six pairwise apolar linearly independent nondegenerate ternary quadratic form
s. These are permuted by the Valentiner group
.
Linear algebra
Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
and projective geometry
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts...
, Gerbaldi's theorem, proved by , states that one can find six pairwise apolar linearly independent nondegenerate ternary quadratic form
Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example,4x^2 + 2xy - 3y^2\,\!is a quadratic form in the variables x and y....
s. These are permuted by the Valentiner group
Valentiner group
In mathematics, the Valentiner group is the perfect triple cover of the alternating group on 6 points, and is a group of order 1080. It was found by in the form of an action of A6 on the complex projective plane, and was studied further by ....
.