In
linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as:
:a_1x_1+\cdots +a_nx_n=b,
linear maps such as:
:(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n,
and their representations in vector spaces and through matrices.
...
and
projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pro ...
, Gerbaldi's theorem, proved by , states that one can find six pairwise apolar
linearly independent
In the theory of vector spaces, a set of vectors is said to be if there is a nontrivial linear combination of the vectors that equals the zero vector. If no such linear combination exists, then the vectors are said to be . These concepts are ...
nondegenerate ternary
quadratic form
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example,
:4x^2 + 2xy - 3y^2
is a quadratic form in the variables and . The coefficients usually belong to a ...
s. These are permuted by the
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 ''A''6 on the complex projective plane, and was studied further by .
...
.
References
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Quadratic forms
Theorems in linear algebra
Theorems in projective geometry
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