Constructing a permutation matrix

General Usage
7

The trouble is relatively minimal, at least to get the basics working:

struct PermutationMatrix <: AbstractMatrix{Bool}
    p::Vector{Int}
end

Base.size(P::PermutationMatrix) = (length(P.p), length(P.p))
Base.getindex(P::PermutationMatrix, i::Integer, j::Integer) = i == P.p[j]

Base.:*(P::PermutationMatrix, A::AbstractMatrix) = A[P.p, :]
Base.:*(A::AbstractMatrix, P::PermutationMatrix) = A[:, P.p]

julia> P = PermutationMatrix([2, 1, 4, 3])
4×4 PermutationMatrix:
 0  1  0  0
 1  0  0  0
 0  0  0  1
 0  0  1  0

julia> A = Matrix(reshape(1:16, 4, 4))
4×4 Matrix{Int64}:
 1  5   9  13
 2  6  10  14
 3  7  11  15
 4  8  12  16

julia> P * A
4×4 Matrix{Int64}:
 2  6  10  14
 1  5   9  13
 4  8  12  16
 3  7  11  15

julia> A * P
4×4 Matrix{Int64}:
 5  1  13   9
 6  2  14  10
 7  3  15  11
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