diff --git a/src/TracedRNumber.jl b/src/TracedRNumber.jl
index 8a5bb307ea..575c53c7eb 100644
--- a/src/TracedRNumber.jl
+++ b/src/TracedRNumber.jl
@@ -567,13 +567,31 @@ Base.Math._log(x::TracedRNumber, base, ::Symbol) = log(x) / log(Reactant._unwrap
 Base.isreal(::TracedRNumber) = false
 Base.isreal(::TracedRNumber{<:Real}) = true
 
+Base.isinteger(x::TracedRNumber{<:Integer}) = true
+Base.isinteger(x::TracedRNumber{<:AbstractFloat}) = x - trunc(x) == zero(x)
+
+Base.isodd(x::TracedRNumber) = isodd(real(x))
+function Base.isodd(x::TracedRNumber{<:Real})
+    return (
+        isinteger(x) &
+        !iszero(
+            rem(
+                Reactant.promote_to(TracedRNumber{Int}, x),
+                Reactant.promote_to(TracedRNumber{Int}, 2),
+            ),
+        )
+    )
+end
+
 Base.iseven(x::TracedRNumber) = iseven(real(x))
 function Base.iseven(x::TracedRNumber{<:Real})
-    return iszero(
-        rem(
-            Reactant.promote_to(TracedRNumber{Int}, x),
-            Reactant.promote_to(TracedRNumber{Int}, 2),
-        ),
+    return (
+        isinteger(x) & iszero(
+            rem(
+                Reactant.promote_to(TracedRNumber{Int}, x),
+                Reactant.promote_to(TracedRNumber{Int}, 2),
+            ),
+        )
     )
 end
 
diff --git a/src/stdlibs/LinearAlgebra.jl b/src/stdlibs/LinearAlgebra.jl
index fa8285e630..b92a5d1177 100644
--- a/src/stdlibs/LinearAlgebra.jl
+++ b/src/stdlibs/LinearAlgebra.jl
@@ -5,8 +5,7 @@ using ..Reactant: Reactant, Ops
 using ..Reactant:
     TracedRArray, TracedRNumber, AnyTracedRArray, AnyTracedRMatrix, AnyTracedRVector
 using ..Reactant: call_with_reactant
-using ReactantCore: ReactantCore
-using ReactantCore: materialize_traced_array
+using ReactantCore: ReactantCore, materialize_traced_array
 using Reactant_jll: Reactant_jll
 
 using ..TracedUtils: TracedUtils, get_mlir_data, set_mlir_data!
@@ -657,6 +656,8 @@ struct GeneralizedLU{T,S<:AbstractArray,P<:AbstractArray,I<:Union{AbstractArray,
     info::I
 end
 
+Base.size(lu::GeneralizedLU) = size(lu.factors)
+
 Base.ndims(lu::GeneralizedLU) = ndims(lu.factors)
 
 function GeneralizedLU(factors::S, ipiv::P, perm::P, info::I) where {S,P,I}
@@ -729,6 +730,26 @@ function LinearAlgebra.ldiv!(
     return B
 end
 
+function LinearAlgebra.det(lu::GeneralizedLU{T,<:AbstractMatrix}) where {T}
+    n = LinearAlgebra.checksquare(lu)
+    # TODO: check for non-singular matrices
+
+    P = prod(LinearAlgebra.diag(lu.factors))
+    return ifelse(isodd(sum(lu.ipiv[1:n] .!= (1:n))), -one(T), one(T)) * P
+end
+
+function LinearAlgebra.logabsdet(lu::GeneralizedLU{T,<:AbstractMatrix}) where {T}
+    n = LinearAlgebra.checksquare(lu)
+    Treal = real(T)
+    # TODO: check for non-singular matrices
+
+    d = LinearAlgebra.diag(lu.factors)
+    absdet = sum(log ∘ abs, d)
+    P = prod(sign, d)
+    s = ifelse(isodd(sum(lu.ipiv[1:n] .!= (1:n))), -one(Treal), one(Treal)) * P
+    return absdet, s
+end
+
 for f_wrapper in (LinearAlgebra.TransposeFactorization, LinearAlgebra.AdjointFactorization),
     aType in (:AbstractVecOrMat, :AbstractArray)
 
@@ -795,4 +816,18 @@ for AT in (
     end
 end
 
+LinearAlgebra._istriu(A::AnyTracedRMatrix, k) = all(iszero, overloaded_tril(A, k - 1))
+LinearAlgebra._istril(A::AnyTracedRMatrix, k) = all(iszero, overloaded_triu(A, k + 1))
+
+# Only needed because we lack automatic if tracing
+function LinearAlgebra.det(A::AnyTracedRMatrix)
+    # FIXME: using @trace here produces the cryptic UndefVarError
+    return LinearAlgebra.det(LinearAlgebra.lu(A; check=false))
+end
+
+function LinearAlgebra.logabsdet(A::AnyTracedRMatrix)
+    # FIXME: using @trace here produces the cryptic UndefVarError
+    return LinearAlgebra.logabsdet(LinearAlgebra.lu(A; check=false))
+end
+
 end
diff --git a/test/integration/linear_algebra.jl b/test/integration/linear_algebra.jl
index 2bab0b7366..ea05cfbf0f 100644
--- a/test/integration/linear_algebra.jl
+++ b/test/integration/linear_algebra.jl
@@ -432,3 +432,35 @@ end
             1e-2
     end
 end
+
+@testset "istriu" begin
+    x = Reactant.TestUtils.construct_test_array(Float32, 8, 8)
+    x_triu = triu(x, 4)
+    x_triu_ra = Reactant.to_rarray(x_triu)
+    @test Bool(@jit(LinearAlgebra.istriu(x_triu_ra, 4)))
+    @test Bool(@jit(LinearAlgebra.istriu(x_triu_ra, 3)))
+    @test !Bool(@jit(LinearAlgebra.istriu(x_triu_ra, 5)))
+end
+
+@testset "istril" begin
+    x = Reactant.TestUtils.construct_test_array(Float32, 8, 8)
+    x_tril = tril(x, -4)
+    x_tril_ra = Reactant.to_rarray(x_tril)
+    @test Bool(@jit(LinearAlgebra.istril(x_tril_ra, -4)))
+    @test Bool(@jit(LinearAlgebra.istril(x_tril_ra, -3)))
+    @test !Bool(@jit(LinearAlgebra.istril(x_tril_ra, -5)))
+end
+
+@testset "det" begin
+    x = Reactant.TestUtils.construct_test_array(Float32, 8, 8)
+    x_ra = Reactant.to_rarray(x)
+
+    res_ra = @jit LinearAlgebra.logabsdet(x_ra)
+    res = LinearAlgebra.logabsdet(x)
+    @test res_ra[1] ≈ res[1]
+    @test res_ra[2] ≈ res[2]
+
+    res_ra = @jit LinearAlgebra.det(x_ra)
+    res = LinearAlgebra.det(x)
+    @test res_ra ≈ res
+end