Decompositions of linear spaces induced by bilinear maps

作者：Calderon Martin Antonio J

来源：Linear Algebra and Its Applications, 2018, 542: 209-224.

DOI：10.1016/j.laa.2017.04.029

• Linear space
• Bilinear map
• Orthogonality
• Invariant subspace
• Decomposition theorem

Let V be an arbitrary linear space and f : V x V -> V a bilinear map. We show that, for any choice of basis B of V, the bilinear map f induces on V a decomposition
V = circle plus V-j is an element of J(j)
as a direct sum of linear subspaces, which is f-orthogonal in the sense
f (V-j, V-k) = 0
when j not equal k, and in such a way that any V-j is strongly f-invariant in the sense
f (V-j, V) + f (V, V-j) subset of V-j.
We also characterize the f-simplicity of any V-j. Finally, an application to the structure theory of arbitrary algebras is also provided.

• 出版日期2018-4-1