Overload Base.literal_pow for AbstractQ (#54010)

(cherry picked from commit b9aeafa)

Author: dkarrasch

stdlib/LinearAlgebra/src/abstractq.jl

@@ -18,6 +18,10 @@ transpose(Q::AbstractQ{<:Real}) = AdjointQ(Q)
 transpose(Q::AbstractQ) = error("transpose not implemented for $(typeof(Q)). Consider using adjoint instead of transpose.")
 adjoint(adjQ::AdjointQ) = adjQ.Q
 
+(^)(Q::AbstractQ, p::Integer) = p < 0 ? power_by_squaring(inv(Q), -p) : power_by_squaring(Q, p)
+@inline Base.literal_pow(::typeof(^), Q::AbstractQ, ::Val{1}) = Q
+@inline Base.literal_pow(::typeof(^), Q::AbstractQ, ::Val{-1}) = inv(Q)
+
 # promotion with AbstractMatrix, at least for equal eltypes
 promote_rule(::Type{<:AbstractMatrix{T}}, ::Type{<:AbstractQ{T}}) where {T} =
     (@inline; Union{AbstractMatrix{T},AbstractQ{T}})

stdlib/LinearAlgebra/test/abstractq.jl

@@ -39,6 +39,12 @@ n = 5
         @test Q'*I ≈ Q.Q'*I rtol=2eps(real(T))
         @test I*Q ≈ Q.Q*I rtol=2eps(real(T))
         @test I*Q' ≈ I*Q.Q' rtol=2eps(real(T))
+        @test Q^3 ≈ Q*Q*Q
+        @test Q^2 ≈ Q*Q
+        @test Q^1 == Q
+        @test Q^(-1) == Q'
+        @test (Q')^(-1) == Q
+        @test (Q')^2 ≈ Q'*Q'
         @test abs(det(Q)) ≈ 1
         @test logabsdet(Q)[1] ≈ 0 atol=2n*eps(real(T))
         y = rand(T, n)