A home for weird matrices that do not fit in anywhere else.
julia> SkewTridiagonal(1:10)
11×11 SkewTridiagonal{Int64,UnitRange{Int64}}:
⋅ -1 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
1 ⋅ -2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ 2 ⋅ -3 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ 3 ⋅ -4 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ 4 ⋅ -5 ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ 5 ⋅ -6 ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ 6 ⋅ -7 ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 7 ⋅ -8 ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 8 ⋅ -9 ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 9 ⋅ -10
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 10 ⋅
julia> OneBlockMatrix(Matrix(reshape(1:15, 5, 3)), 10, 20)
10×20 OneBlockMatrix{Int64,Array{Int64,2}}:
1 6 11 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
2 7 12 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
3 8 13 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
4 9 14 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
5 10 15 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅OneBlockMatrix are also closed under some operations:
julia> N = 7
7
julia> A = OneBlockMatrix(Matrix(reshape(1:16, 4,4)), N, N)
7×7 OneBlockMatrix{Int64,Array{Int64,2}}:
1 5 9 13 ⋅ ⋅ ⋅
2 6 10 14 ⋅ ⋅ ⋅
3 7 11 15 ⋅ ⋅ ⋅
4 8 12 16 ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
julia> o = ones(Int, N)
7-element Array{Int64,1}:
1
1
1
1
1
1
1
julia> T = Tridiagonal(o[2:end], 2o, 3o[2:end])
7×7 Tridiagonal{Int64,Array{Int64,1}}:
2 3 ⋅ ⋅ ⋅ ⋅ ⋅
1 2 3 ⋅ ⋅ ⋅ ⋅
⋅ 1 2 3 ⋅ ⋅ ⋅
⋅ ⋅ 1 2 3 ⋅ ⋅
⋅ ⋅ ⋅ 1 2 3 ⋅
⋅ ⋅ ⋅ ⋅ 1 2 3
⋅ ⋅ ⋅ ⋅ ⋅ 1 2
julia> T*A
7×7 OneBlockMatrix{Int64,Array{Int64,2}}:
8 28 48 68 ⋅ ⋅ ⋅
14 38 62 86 ⋅ ⋅ ⋅
20 44 68 92 ⋅ ⋅ ⋅
11 23 35 47 ⋅ ⋅ ⋅
4 8 12 16 ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
julia> A^2
7×7 OneBlockMatrix{Int64,Array{Int64,2}}:
90 202 314 426 ⋅ ⋅ ⋅
100 228 356 484 ⋅ ⋅ ⋅
110 254 398 542 ⋅ ⋅ ⋅
120 280 440 600 ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅