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The methods in InfiniteArrays.jl and InfiniteLinearAlgebra.jl don't currently seem to agree on what is a diagonal and what is a banded matrix. To give some concrete examples:
A minimal working example for Diagonal is
julia> LinearAlgebra.isdiag(InfiniteArrays.Diagonal(0:∞))
true
but the following never finishes computing, i.e. does not even return false:
julia> LinearAlgebra.isdiag(InfiniteLinearAlgebra.BandedMatrix(0=>(0:∞)))
Furthermore, we have a similar situation for banded matrix types:
julia> InfiniteLinearAlgebra.BandedMatrix(0 => (1:∞)) isa InfiniteLinearAlgebra.BandedMatrix
true
julia> InfiniteArrays.Diagonal(1:∞) isa InfiniteLinearAlgebra.BandedMatrix
false
What one wants these to evaluate to might be up to the design philosophy between the packages to some degree but the current behavior does seem odd.
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