Biorthogonal system
In mathematics, a biorthogonal system is a pair of indexed families of vectors
such that
where E and F form a pair of topological vector spaces that are in duality, is a bilinear mapping and is the Kronecker delta.
An example is the pair of sets of respectively left and right eigenvectors of a matrix, indexed by eigenvalue, if the eigenvalues are distinct.
A biorthogonal system in which and is an orthonormal system.Projection
Related to a biorthogonal system is the projection
where ; its image is the linear span of, and the kernel is.Construction
Given a possibly non-orthogonal set of vectors and the projection related is
where is the matrix with entries.
- , and then is a biorthogonal system.
