## Subspaces.jl

Vector subspaces in Julia
Author dstahlke
Popularity
1 Star
Updated Last
2 Years Ago
Started In
December 2020

# 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```