diff --git a/src/stdlibs/LinearAlgebra.jl b/src/stdlibs/LinearAlgebra.jl
index 7ff8bcbebd..445105c1c9 100644
--- a/src/stdlibs/LinearAlgebra.jl
+++ b/src/stdlibs/LinearAlgebra.jl
@@ -397,6 +397,67 @@ function LinearAlgebra._kron!(C::AnyTracedRMatrix, A::AnyTracedRMatrix, B::AnyTr
     return C
 end
 
+function LinearAlgebra.dot(x::TracedRArray{T}, y::TracedRArray) where {T}
+    lx = length(x)
+    if lx != length(y)
+         throw(DimensionMismatch(lazy"first array has length $(lx) which does not match the length of the second, $(length(y))."))
+    end
+    
+    if T <: Complex
+        x = Ops.conj(x)
+    end
+    
+    return Ops.dot_general(x, y; contracting_dimensions = [[1], [1]]) 
+end
+
+function LinearAlgebra.cross(a::AnyTracedRVector{T1}, b::AnyTracedRVector{T2}) where {T1, T2}
+    if !(length(a) == length(b) == 3)
+         throw(DimensionMismatch("cross product is only defined for vectors of length 3"))
+    end
+    a = materialize_traced_array(a)
+    b = materialize_traced_array(b)
+
+    a1, a2, a3 = a
+    b1, b2, b3 = b
+    c = [a2*b3-a3*b2, a3*b1-a1*b3, a1*b2-a2*b1]
+    
+    T = promote_type(T1, T2)
+
+    return TracedUtils.promote_to(TracedRArray{T, 1}, c)
+end
+
+function LinearAlgebra.adjoint!(B::AnyTracedRVector{T1}, A::AnyTracedRMatrix{T2}) where {T1, T2}
+    LinearAlgebra.check_transpose_axes((size(B,1), size(B,2)), size(A))
+    T = promote_type(T1, T2)
+    if T <: Complex
+        A = Ops.conj(A)
+    end
+    AT = TracedUtils.promote_to(TracedRArray{T, 2}, A)
+    set_mlir_data!(B, get_mlir_data(Ops.reshape(AT, length(B))))
+    return B
+end
+
+function LinearAlgebra.adjoint!(B::AnyTracedRMatrix{T1}, A::AnyTracedRVector{T2}) where {T1, T2}
+    LinearAlgebra.check_transpose_axes(size(B), (size(A, 1), size(A, 2)))
+    T = promote_type(T1, T2)
+    if T <: Complex
+        A = Ops.conj(A)
+    end
+    set_mlir_data!(B, get_mlir_data(Ops.broadcast_in_dim(A, [2], [1, length(A)])))
+    return B
+end
+
+function LinearAlgebra.adjoint!(B::AnyTracedRMatrix{T1}, A::AnyTracedRMatrix{T2}) where {T1, T2}
+    LinearAlgebra.check_transpose_axes(size(B), size(A))
+    T = promote_type(T1, T2)
+    if T <: Complex
+        A = Ops.conj(A)
+    end
+    AT = TracedUtils.promote_to(TracedRArray{T, 2}, Ops.transpose(A, [2,1]))
+    set_mlir_data!(B, get_mlir_data(AT))
+    return B
+end
+                  
 function LinearAlgebra.axpy!(α::Number, x::TracedRArray{T}, y::TracedRArray{T}) where {T}
     if length(x) != length(y)
         throw(DimensionMismatch(lazy"x has length $(length(x)), but y has length $(length(y))"))
diff --git a/test/integration/linear_algebra.jl b/test/integration/linear_algebra.jl
index 114b352524..516c317a66 100644
--- a/test/integration/linear_algebra.jl
+++ b/test/integration/linear_algebra.jl
@@ -184,6 +184,88 @@ end
     end
 end
 
+@testset "dot" begin
+    a = [1, 2, 3, 4]
+    b = [-2, 5, 6, 7]
+    a_ra = Reactant.to_rarray(a)
+    b_ra = Reactant.to_rarray(b)
+
+    @test @jit dot(a_ra, b_ra) ≈ dot(a, b)
+
+    a = rand(Int64, 4)
+    b = rand(4)
+    a_ra = Reactant.to_rarray(a)
+    b_ra = Reactant.to_rarray(b)
+    
+    @test @jit dot(a_ra, b_ra) ≈ dot(a, b)
+
+    a = rand(Complex{Float64}, 4)
+    b = rand(Complex{Float64}, 4)
+    a_ra = Reactant.to_rarray(a)
+    b_ra = Reactant.to_rarray(b)
+    ab_ra = @jit dot(a_ra, b_ra)
+    ab = dot(a,b)
+    
+    @test ab_ra ≈ ab 
+end
+
+@testset "cross" begin
+    a = [1, 2, 3]
+    b = [-2, 5, 7]
+    a_ra = Reactant.to_rarray(a)
+    b_ra = Reactant.to_rarray(b)
+
+    @test @jit cross(a_ra, b_ra) ≈ cross(a, b)
+
+    a = rand(Int64, 3)
+    b = rand(3)
+    a_ra = Reactant.to_rarray(a)
+    b_ra = Reactant.to_rarray(b)
+    
+    @test @jit dot(a_ra, b_ra) ≈ dot(a, b)
+
+    a = rand(Complex{Float64}, 3)
+    b = rand(Complex{Float64}, 3)
+    a_ra = Reactant.to_rarray(a)
+    b_ra = Reactant.to_rarray(b)
+
+    @test @jit cross(a_ra, b_ra) ≈ cross(a,b)
+end  
+
+@testset "adjoint!" begin
+    v = zeros(5)
+    M = rand(1, 5)
+    v_ra = Reactant.to_rarray(v)
+    M_ra = Reactant.to_rarray(M)
+
+    @jit adjoint!(v_ra, M_ra)
+    @test v_ra ≈ adjoint!(v, M)
+
+    v = rand(7)
+    M = zeros(1, 7)
+    v_ra = Reactant.to_rarray(v)
+    M_ra = Reactant.to_rarray(M)
+
+    @jit adjoint!(M_ra, v_ra)
+    @test M_ra ≈ adjoint!(M, v)
+
+    A = [1 2; 3 4; 5 6]
+    B = fill(Float64(0), (2,3))
+    A_ra = Reactant.to_rarray(A)
+    B_ra = Reactant.to_rarray(B)
+    
+    @jit adjoint!(B_ra, A_ra)
+    @test B_ra ≈ adjoint!(B, A)
+
+    A = rand(Complex{Float64}, (2, 3))
+    B = rand(Complex{Float64}, (3, 2))
+    A_ra = Reactant.to_rarray(A)
+    B_ra = Reactant.to_rarray(B)
+    
+    @jit adjoint!(B_ra, A_ra)
+    @test B_ra ≈ adjoint!(B, A)
+end
+
 @testset "axpy!" begin
     α = 3
     x = rand(Int64, 4)
@@ -220,7 +302,6 @@ end
 
     @jit axpy!(α, x_ra, y_ra)
     @test y_ra ≈ axpy!(α, x, y)
-
 end
 
 @testset "axpby!" begin
@@ -262,8 +343,4 @@ end
 
     @jit axpby!(α, x_ra, β, y_ra)
     @test y_ra ≈ axpby!(α, x, β, y)
-
 end
-
-
-