diff --git a/base/linalg/symmetric.jl b/base/linalg/symmetric.jl
index f23825940791c..611bb2adb5191 100644
--- a/base/linalg/symmetric.jl
+++ b/base/linalg/symmetric.jl
@@ -107,6 +107,21 @@ end
     r
 end
 
+function setindex!(A::Symmetric, v, i::Integer, j::Integer)
+    i == j || throw(ArgumentError("Cannot set a non-diagonal index in a symmetric matrix"))
+    setindex!(A.data, v, i, j)
+end
+
+function setindex!(A::Hermitian, v, i::Integer, j::Integer)
+    if i != j
+        throw(ArgumentError("Cannot set a non-diagonal index in a Hermitian matrix"))
+    elseif !isreal(v)
+        throw(ArgumentError("Cannot set a diagonal entry in a Hermitian matrix to a nonreal value"))
+    else
+        setindex!(A.data, v, i, j)
+    end
+end
+
 similar{T}(A::Symmetric, ::Type{T}) = Symmetric(similar(A.data, T))
 # Hermitian version can be simplified when check for imaginary part of
 # diagonal in Hermitian has been removed
@@ -133,6 +148,25 @@ convert{T}(::Type{AbstractMatrix{T}}, A::Hermitian) = Hermitian(convert(Abstract
 
 copy{T,S}(A::Symmetric{T,S}) = (B = copy(A.data); Symmetric{T,typeof(B)}(B,A.uplo))
 copy{T,S}(A::Hermitian{T,S}) = (B = copy(A.data); Hermitian{T,typeof(B)}(B,A.uplo))
+
+function copy!(dest::Symmetric, src::Symmetric)
+    if src.uplo == dest.uplo
+        copy!(dest.data, src.data)
+    else
+        transpose!(dest.data, src.data)
+    end
+    return dest
+end
+
+function copy!(dest::Hermitian, src::Hermitian)
+    if src.uplo == dest.uplo
+        copy!(dest.data, src.data)
+    else
+        ctranspose!(dest.data, src.data)
+    end
+    return dest
+end
+
 ishermitian(A::Hermitian) = true
 ishermitian{T<:Real,S}(A::Symmetric{T,S}) = true
 ishermitian{T<:Complex,S}(A::Symmetric{T,S}) = all(imag(A.data) .== 0)
@@ -218,6 +252,13 @@ A_mul_B!{T<:BlasComplex,S<:StridedMatrix}(C::StridedMatrix{T}, A::StridedMatrix{
 *(A::HermOrSym, B::HermOrSym) = full(A)*full(B)
 *(A::StridedMatrix, B::HermOrSym) = A*full(B)
 
+for T in (:Symmetric, :Hermitian), op in (:+, :-, :*, :/)
+    # Deal with an ambiguous case
+    @eval ($op)(A::$T, x::Bool) = ($T)(($op)(A.data, x), Symbol(A.uplo))
+    S = T == :Hermitian ? :Real : :Number
+    @eval ($op)(A::$T, x::$S) = ($T)(($op)(A.data, x), Symbol(A.uplo))
+end
+
 bkfact(A::HermOrSym) = bkfact(A.data, Symbol(A.uplo), issymmetric(A))
 factorize(A::HermOrSym) = bkfact(A)
 
diff --git a/test/linalg/symmetric.jl b/test/linalg/symmetric.jl
index 452637898f361..80e1976abad7b 100644
--- a/test/linalg/symmetric.jl
+++ b/test/linalg/symmetric.jl
@@ -250,3 +250,36 @@ let a = randn(2,2)
     cc = copy(c)
     @test conj!(c) == conj(Array(c))
 end
+
+# 19225
+let X = [1 -1; -1 1]
+    for T in (Symmetric, Hermitian)
+        Y = T(copy(X))
+        _Y = similar(Y)
+        copy!(_Y, Y)
+        @test _Y == Y
+
+        W = T(copy(X), :L)
+        copy!(W, Y)
+        @test W.data == Y.data
+        @test W.uplo != Y.uplo
+
+        W[1,1] = 4
+        @test W == T([4 -1; -1 1])
+        @test_throws ArgumentError (W[1,2] = 2)
+
+        @test Y + I == T([2 -1; -1 2])
+        @test Y - I == T([0 -1; -1 0])
+        @test Y * I == Y
+
+        @test Y + 1 == T([2 0; 0 2])
+        @test Y - 1 == T([0 -2; -2 0])
+        @test Y * 2 == T([2 -2; -2 2])
+        @test Y / 1 == Y
+
+        @test T([true false; false true]) + true == T([2 1; 1 2])
+    end
+
+    @test_throws ArgumentError Hermitian(X) + 2im*I
+    @test_throws ArgumentError Hermitian(X) - 2im*I
+end
diff --git a/test/sparse/sparse.jl b/test/sparse/sparse.jl
index b56ad98a84d97..72aef1cbe1ef0 100644
--- a/test/sparse/sparse.jl
+++ b/test/sparse/sparse.jl
@@ -1635,3 +1635,31 @@ let
     @test isa(abs.(A), SparseMatrixCSC) # representative for _unary_nz2nz_z2z class
     @test isa(exp.(A), Array) # representative for _unary_nz2nz_z2nz class
 end
+
+# 19225
+let X = sparse([1 -1; -1 1])
+    for T in (Symmetric, Hermitian)
+        Y = T(copy(X))
+        _Y = similar(Y)
+        copy!(_Y, Y)
+        @test _Y == Y
+
+        W = T(copy(X), :L)
+        copy!(W, Y)
+        @test W.data == Y.data
+        @test W.uplo != Y.uplo
+
+        W[1,1] = 4
+        @test W == T(sparse([4 -1; -1 1]))
+        @test_throws ArgumentError (W[1,2] = 2)
+
+        @test Y + I == T(sparse([2 -1; -1 2]))
+        @test Y - I == T(sparse([0 -1; -1 0]))
+        @test Y * I == Y
+
+        @test Y + 1 == T(sparse([2 0; 0 2]))
+        @test Y - 1 == T(sparse([0 -2; -2 0]))
+        @test Y * 2 == T(sparse([2 -2; -2 2]))
+        @test Y / 1 == Y
+    end
+end