dstahlke / Subspaces.jl

Vector subspaces in Julia

Subspaces.jl - Vector subspaces in Julia

Subspaces.jl provides a Subspace type for representing linear subspaces of a finite dimensional vector space. Subspaces of matrices or tensors are also supported, as these are vectors in the mathematical sense of the word. Both real and complex base fields are supported.

Example

julia> using Subspaces

julia> S = Subspace([ [1,0,0], [0,1,1] ])
Subspace{Float64} size (3,) dim 2

julia> [1,2,2] ∈ S
true

julia> [1,1,2] ∈ S
false

julia> S.basis
3×2 Array{Float64,2}:
  0.0       1.0
 -0.707107  0.0
 -0.707107  0.0

julia> S | Subspace([ [0,0,1] ])
Subspace{Float64} size (3,) dim 3

julia> S & Subspace([ [1,1,1] ])
Subspace{Float64} size (3,) dim 1

julia> kron(S, S)
Subspace{Float64} size (9,) dim 4

julia> S * S'
Subspace{Float64} size (3, 3) dim 4

julia> Subspace([ ones(3,4,5) ])
Subspace{Float64} size (3, 4, 5) dim 1