SymTridiagonal{<:Matrix} should transpose for sub-diagonal and make diagonal symmetric

[dlfivefifty]

Symmetric with a Matrix{<:Matrix} transposes the argument:

julia> A = Symmetric(fill([1 2; 3 4],3,3));

julia> A[1,1]
2×2 Symmetric{Int64,Array{Int64,2}}:
 1  2
 2  4

julia> A[1,2]
2×2 Array{Int64,2}:
 1  2
 3  4

julia> A[2,1]
2×2 Transpose{Int64,Array{Int64,2}}:
 1  3
 2  4

For consistency, SymTridiagonal should have similar behaviour, but it doesn't:

julia> A = SymTridiagonal(fill([1 2; 3 4],3), fill([1 2; 3 4],2));

julia> A[1,1]
2×2 Array{Int64,2}:
 1  2
 3  4

julia> A[1,2]
2×2 Array{Int64,2}:
 1  2
 3  4

julia> A[2,1]
2×2 Array{Int64,2}:
 1  2
 3  4

[namanbiyani]

Hi, I was planning to contribute towards GSoC 2019. I want to contribute to this issue. Please give some guidelines .

[dlfivefifty]

Probably we want the following behaviour:

julia> A = SymTridiagonal(fill([1 2; 3 4],3), fill([1 2; 3 4],2));

julia> A[1,1]
2×2 Symmetric{Int64,Array{Int64,2}}:
 1  2
 2  4

julia> A[1,2]
2×2 Array{Int64,2}:
 1  2
 3  4

julia> A[2,1]
2×2 Transpose{Int64,Array{Int64,2}}:
 1  3
 2  4

[dkarrasch]

I started being very skeptical about interpreting special matrix structure elementwise, see #610.