Float16 input now gives Float 16 factors for svd,eigen and cholesky.

stdlib/LinearAlgebra/src/cholesky.jl

@@ -388,6 +388,11 @@ true
 cholesky(A::Union{StridedMatrix,RealHermSymComplexHerm{<:Real,<:StridedMatrix}},
     ::Val{false}=Val(false); check::Bool = true) = cholesky!(cholcopy(A); check = check)
 
+function cholesky(A::Union{StridedMatrix{Float16},RealHermSymComplexHerm{Float16,<:StridedMatrix}}, ::Val{false}=Val(false); check::Bool = true)
+    X = cholesky!(cholcopy(A); check = check)
+    return Cholesky{Float16}(X)
+end
+
 
 ## With pivoting
 """

stdlib/LinearAlgebra/src/eigen.jl

@@ -275,6 +275,18 @@ function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortb
     isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
     return eigen!(AA; permute=permute, scale=scale, sortby=sortby, jvl=jvl, jvr=jvr, jce=jce, jcv=jcv)
 end
+function eigen(A::AbstractMatrix{Float16}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby)
+    AA = copy_oftype(A, eigtype(Float16))
+    isdiag(AA) && return eigen(Diagonal(AA); permute=permute, scale=scale, sortby=sortby)
+    A = eigen!(AA; permute=permute, scale=scale, sortby=sortby)
+    if isreal(A.values)
+        Eigen(convert(Vector{Float16}, A.values),
+            convert(AbstractArray{Float16}, A.vectors))
+    else
+        Eigen(convert(Vector{Complex{Float16}}, A.values),
+            convert(AbstractArray{Complex{Float16}}, A.vectors))
+    end
+end
 eigen(x::Number) = Eigen([x], fill(one(x), 1, 1))
 
 """

stdlib/LinearAlgebra/src/svd.jl

@@ -175,6 +175,10 @@ true
 function svd(A::StridedVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T}
     svd!(copy_oftype(A, eigtype(T)), full = full, alg = alg)
 end
+function svd(A::StridedVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T <: Union{Float16,Complex{Float16}}
+    A = svd!(copy_oftype(A, eigtype(T)), full = full, alg = alg)
+    return SVD{T}(A)
+end
 function svd(x::Number; full::Bool = false, alg::Algorithm = default_svd_alg(x))
     SVD(x == 0 ? fill(one(x), 1, 1) : fill(x/abs(x), 1, 1), [abs(x)], fill(one(x), 1, 1))
 end

stdlib/LinearAlgebra/test/cholesky.jl

@@ -483,4 +483,13 @@ end
     @test F\b == F'\b
 end
 
+@testset "Float16" begin
+    A = Float16[4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
+    B = cholesky(A)
+    @test B isa Cholesky{Float16, Matrix{Float16}}
+    @test B.U isa UpperTriangular{Float16, Matrix{Float16}}
+    @test B.L isa LowerTriangular{Float16, Matrix{Float16}}
+    @test B.UL isa UpperTriangular{Float16, Matrix{Float16}}
+end
+
 end # module TestCholesky

stdlib/LinearAlgebra/test/eigen.jl

@@ -177,4 +177,12 @@ end
     @test isequal(eigen(A), eigen(A))
 end
 
+@testset "Float16" begin
+    A = Float16[4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
+    B = eigen(A)
+    @test B isa Eigen{Float16, Float16, Matrix{Float16}, Vector{Float16}, Vector{Float16}}
+    @test B.values isa Vector{Float16}
+    @test B.vectors isa Matrix{Float16}
+end
+
 end # module TestEigen

stdlib/LinearAlgebra/test/svd.jl

@@ -248,4 +248,13 @@ end
     end
 end
 
+@testset "Float16" begin
+    A = Float16[4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
+    B = svd(A)
+    @test B isa SVD{Float16, Float16, Matrix{Float16}}
+    @test B.U isa Matrix{Float16}
+    @test B.Vt isa Matrix{Float16}
+    @test B.S isa Vector{Float16}
+end
+
 end # module TestSVD