diff --git a/stdlib/LinearAlgebra/src/bunchkaufman.jl b/stdlib/LinearAlgebra/src/bunchkaufman.jl
index 8d1ded9bf8111..5a73c656abe33 100644
--- a/stdlib/LinearAlgebra/src/bunchkaufman.jl
+++ b/stdlib/LinearAlgebra/src/bunchkaufman.jl
@@ -297,6 +297,17 @@ end
 Base.propertynames(B::BunchKaufman, private::Bool=false) =
     (:p, :P, :L, :U, :D, (private ? fieldnames(typeof(B)) : ())...)
 
+function Base.:(==)(B1::BunchKaufman, B2::BunchKaufman)
+    # check for the equality between properties instead of fields
+    B1.p == B2.p || return false
+    if B1.uplo == 'L'
+        B1.L == B2.L || return false
+    else
+        B1.U == B2.U || return false
+    end
+    return (B1.D == B2.D)
+end
+
 function getproperties!(B::BunchKaufman{T,<:StridedMatrix}) where {T<:BlasFloat}
     # NOTE: Unlike in the 'getproperty' function, in this function L/U and D are computed in place.
     if B.rook
diff --git a/stdlib/LinearAlgebra/src/cholesky.jl b/stdlib/LinearAlgebra/src/cholesky.jl
index de418fe8426a5..510ec2f2a341a 100644
--- a/stdlib/LinearAlgebra/src/cholesky.jl
+++ b/stdlib/LinearAlgebra/src/cholesky.jl
@@ -546,6 +546,11 @@ end
 Base.propertynames(F::Cholesky, private::Bool=false) =
     (:U, :L, :UL, (private ? fieldnames(typeof(F)) : ())...)
 
+function Base.:(==)(C1::Cholesky, C2::Cholesky)
+    C1.uplo == C2.uplo || return false
+    C1.uplo == 'L' ? (C1.L == C2.L) : (C1.U == C2.U)
+end
+
 function getproperty(C::CholeskyPivoted{T}, d::Symbol) where {T}
     Cfactors = getfield(C, :factors)
     Cuplo    = getfield(C, :uplo)
@@ -569,6 +574,11 @@ end
 Base.propertynames(F::CholeskyPivoted, private::Bool=false) =
     (:U, :L, :p, :P, (private ? fieldnames(typeof(F)) : ())...)
 
+function Base.:(==)(C1::CholeskyPivoted, C2::CholeskyPivoted)
+    (C1.uplo == C2.uplo && C1.p == C2.p) || return false
+    C1.uplo == 'L' ? (C1.L == C2.L) : (C1.U == C2.U)
+end
+
 issuccess(C::Union{Cholesky,CholeskyPivoted}) = C.info == 0
 
 adjoint(C::Union{Cholesky,CholeskyPivoted}) = C
diff --git a/stdlib/LinearAlgebra/src/eigen.jl b/stdlib/LinearAlgebra/src/eigen.jl
index d1d2a156b1ed4..e0124f2e9d870 100644
--- a/stdlib/LinearAlgebra/src/eigen.jl
+++ b/stdlib/LinearAlgebra/src/eigen.jl
@@ -658,14 +658,19 @@ function show(io::IO, mime::MIME{Symbol("text/plain")}, F::Union{Eigen,Generaliz
     show(io, mime, F.vectors)
 end
 
-function Base.hash(F::Eigen, h::UInt)
-    return hash(F.values, hash(F.vectors, hash(Eigen, h)))
-end
-function Base.:(==)(A::Eigen, B::Eigen)
-    return A.values == B.values && A.vectors == B.vectors
-end
-function Base.isequal(A::Eigen, B::Eigen)
-    return isequal(A.values, B.values) && isequal(A.vectors, B.vectors)
+_equalcheck(f, Avalues, Avectors, Bvalues, Bvectors) = f(Avalues, Bvalues) && f(Avectors, Bvectors)
+for T in (Eigen, GeneralizedEigen)
+    @eval begin
+        function Base.hash(F::$T, h::UInt)
+            return hash(F.values, hash(F.vectors, hash($T, h)))
+        end
+        function Base.:(==)(A::$T, B::$T)
+            return _equalcheck(==, A..., B...)
+        end
+        function Base.isequal(A::$T, B::$T)
+            return _equalcheck(isequal, A..., B...)
+        end
+    end
 end
 
 # Conversion methods
diff --git a/stdlib/LinearAlgebra/test/cholesky.jl b/stdlib/LinearAlgebra/test/cholesky.jl
index cce26af40108b..af7eed3f5a764 100644
--- a/stdlib/LinearAlgebra/test/cholesky.jl
+++ b/stdlib/LinearAlgebra/test/cholesky.jl
@@ -553,6 +553,7 @@ end
         M = Matrix{BigFloat}(undef, 2, 2)
         M[1,1] = M[2,2] = M[1+(uplo=='L'), 1+(uplo=='U')] = 3
         C = Cholesky(M, uplo, 0)
+        @test C == C
         @test C.L == C.U'
         # parameters are arbitrary
         C = CholeskyPivoted(M, uplo, [1,2], 2, 0.0, 0)
diff --git a/stdlib/LinearAlgebra/test/eigen.jl b/stdlib/LinearAlgebra/test/eigen.jl
index 73d9147a82a09..174deffbc53e9 100644
--- a/stdlib/LinearAlgebra/test/eigen.jl
+++ b/stdlib/LinearAlgebra/test/eigen.jl
@@ -212,10 +212,22 @@ end
 end
 
 @testset "equality of eigen factorizations" begin
-    A = randn(3, 3)
-    @test eigen(A) == eigen(A)
-    @test hash(eigen(A)) == hash(eigen(A))
-    @test isequal(eigen(A), eigen(A))
+    A1 = Float32[1 0; 0 2]
+    A2 = Float64[1 0; 0 2]
+    EA1 = eigen(A1)
+    EA2 = eigen(A2)
+    @test EA1 == EA2
+    @test hash(EA1) == hash(EA2)
+    @test isequal(EA1, EA2)
+
+    # trivial RHS to ensure that values match exactly
+    B1 = Float32[1 0; 0 1]
+    B2 = Float64[1 0; 0 1]
+    EA1B1 = eigen(A1, B1)
+    EA2B2 = eigen(A2, B2)
+    @test EA1B1 == EA2B2
+    @test hash(EA1B1) == hash(EA2B2)
+    @test isequal(EA1B1, EA2B2)
 end
 
 @testset "Float16" begin
diff --git a/stdlib/LinearAlgebra/test/factorization.jl b/stdlib/LinearAlgebra/test/factorization.jl
index 72233293ff515..f80c5197836a1 100644
--- a/stdlib/LinearAlgebra/test/factorization.jl
+++ b/stdlib/LinearAlgebra/test/factorization.jl
@@ -37,8 +37,8 @@ using Test, LinearAlgebra
         return x isa AbstractArray{Float64} ? Float64.(Float32.(x)) : x
     end...)
 
-    @test F == G broken=!(f === eigen || f === qr)
-    @test isequal(F, G) broken=!(f === eigen || f === qr)
+    @test F == G broken=!(f === eigen || f === qr || f == bunchkaufman || f == cholesky || F isa CholeskyPivoted)
+    @test isequal(F, G) broken=!(f === eigen || f === qr || f == bunchkaufman || f == cholesky || F isa CholeskyPivoted)
     @test hash(F) == hash(G)
 end