Combinatorics

Discrete mathematics

Annihilator

Pure mathematics

Algebraically closed field

Bilinear interpolation

Dimension (graph theory)

Mathematics

Crystallography

Codimension

Operating system

Crystal structure

Statistics

Algebra over a field

Mathematical analysis

Chemistry

Isomorphism (crystallography)

Space (punctuation)

Computer science

Field (mathematics)

Base (topology)

Bilinear form

Linear and Multilinear Algebra

Let ${\mathbb V}$ be an $n$-dimensional linear space over an algebraically closed base field. We provide a classification, up to equivalence, of all of the bilinear maps $f:{\mathbb V} \times {\mathbb V} \to {\mathbb V}$ such that $dim(rad(f)) =n-2$. This is equivalent to give a complete classification (up to isomorphism) of all $n$-dimensional algebras with annihilator of dimension $n-2$ or, in other words, a classification of the annihilator extensions of all $2$-dimensional algebras.

On the classification of bilinear maps with radical of a fixed codimension