fix README and add a bunch of other dispatches for issingular

Author: ChrisRackauckas

README.md

@@ -67,9 +67,7 @@ cheaply.
 
 ## issingular(A)
 
-Check singularity by factorization or checking zeros of structured matrices.
-
-*Warning*: `rank` is a better choice for some matrices.
+Return an instance of the LU factorization object with the correct type cheaply.
 
 ## List of things to add
 

src/ArrayInterface.jl

@@ -111,9 +111,14 @@ has_sparsestruct(x::Type{<:SymTridiagonal}) = true
 
 Determine whether a given abstract matrix is singular.
 """
+issingular(A::AbstractMatrix) = issingular(Matrix(A))
+issingular(A::AbstractSparseMatrix) = !issuccess(lu(A, check=false))
 issingular(A::Matrix) = !issuccess(lu(A, check=false))
 issingular(A::UniformScaling) = A.λ == 0
 issingular(A::Diagonal) = any(iszero,A.diag)
+issingular(B::Bidiagonal) = any(iszero, A.dv)
+issingular(S::SymTridiagonal) = diaganyzero(iszero, ldlt(S).data)
+issingular(T::Tridiagonal) = !issuccess(lu(A, check=false))
 issingular(A::Union{Hermitian,Symmetric}) = diaganyzero(bunchkaufman(A, check=false).LD)
 issingular(A::Union{LowerTriangular,UpperTriangular}) = diaganyzero(A.data)
 issingular(A::Union{UnitLowerTriangular,UnitUpperTriangular}) = false