Computing the rank of a symbolic matrix in Julia

General Usage
,
7

UPDATE. SymEngine and SymPy don’t seem to generate symbolic matrix inverses either, nor eigenvalues.

This isn’t quite true:

julia> using SymPy

julia> M = Sym["a$i$j" for i in 1:2, j in 1:2]
2×2 Array{Sym,2}:
 a₁₁  a₁₂
 a₂₁  a₂₂

julia> inv(M)
2×2 Array{Sym,2}:
  a22/(a11*a22 - a12*a21)  -a12/(a11*a22 - a12*a21)
 -a21/(a11*a22 - a12*a21)   a11/(a11*a22 - a12*a21)

julia> using LinearAlgebra

julia> eigvals(M) # also M.eigenvals()
2-element Array{Sym,1}:
 a11/2 + a22/2 - sqrt(a11^2 - 2*a11*a22 + 4*a12*a21 + a22^2)/2
 a11/2 + a22/2 + sqrt(a11^2 - 2*a11*a22 + 4*a12*a21 + a22^2)/2

julia> eigvecs(M) # also M.eigenvects()
2×2 Array{Sym,2}:
 -2*a12/(a11 - a22 + sqrt(a11^2 - 2*a11*a22 + 4*a12*a21 + a22^2))  …  -2*a12/(a11 - a22 - sqrt(a11^2 - 2*a11*a22 + 4*a12*a21 + a22^2))
                                                                1                                                                    1

julia> M.rank()
2
2 Likes