add handling of sqrt() function for empty matrices (#50270)

Author: vmpyr

stdlib/LinearAlgebra/src/dense.jl

@@ -875,7 +875,9 @@ julia> sqrt(A)
 sqrt(::AbstractMatrix)
 
 function sqrt(A::AbstractMatrix{T}) where {T<:Union{Real,Complex}}
-    if ishermitian(A)
+    if checksquare(A) == 0
+        return copy(A)
+    elseif ishermitian(A)
         sqrtHermA = sqrt(Hermitian(A))
         return ishermitian(sqrtHermA) ? copytri!(parent(sqrtHermA), 'U', true) : parent(sqrtHermA)
     elseif istriu(A)

stdlib/LinearAlgebra/test/dense.jl

@@ -1213,6 +1213,11 @@ end
     @test exp(log(A2)) ≈ A2
 end
 
+@testset "sqrt of empty Matrix of type $T" for T in [Int,Float32,Float64,ComplexF32,ComplexF64]
+    @test sqrt(Matrix{T}(undef, 0, 0)) == Matrix{T}(undef, 0, 0)
+    @test_throws DimensionMismatch sqrt(Matrix{T}(undef, 0, 3))
+end
+
 struct TypeWithoutZero end
 Base.zero(::Type{TypeWithoutZero}) = TypeWithZero()
 struct TypeWithZero end