diff --git a/src/nlp_expr.jl b/src/nlp_expr.jl
index 6fe42fcb5ee..ed43347a54a 100644
--- a/src/nlp_expr.jl
+++ b/src/nlp_expr.jl
@@ -1111,3 +1111,30 @@ end
 function MOI.VectorNonlinearFunction(f::Vector{<:AbstractJuMPScalar})
     return MOI.VectorNonlinearFunction(map(moi_function, f))
 end
+
+# LinearAlgebra overloads to throw nicer error messages. These may be changed to
+# return expressions in the future.
+
+function LinearAlgebra.det(::AbstractMatrix{<:AbstractJuMPScalar})
+    return throw(MOI.UnsupportedNonlinearOperator(:det))
+end
+
+function LinearAlgebra.logdet(::AbstractMatrix{<:AbstractJuMPScalar})
+    return throw(MOI.UnsupportedNonlinearOperator(:logdet))
+end
+
+function LinearAlgebra.norm(::AbstractArray{<:AbstractJuMPScalar}, ::Real)
+    return throw(MOI.UnsupportedNonlinearOperator(:norm))
+end
+
+function LinearAlgebra.nullspace(::AbstractVector{<:AbstractJuMPScalar})
+    return throw(MOI.UnsupportedNonlinearOperator(:nullspace))
+end
+
+function LinearAlgebra.nullspace(::AbstractMatrix{<:AbstractJuMPScalar})
+    return throw(MOI.UnsupportedNonlinearOperator(:nullspace))
+end
+
+function LinearAlgebra.qr(::AbstractMatrix{<:AbstractJuMPScalar})
+    return throw(MOI.UnsupportedNonlinearOperator(:qr))
+end
diff --git a/test/test_nlp_expr.jl b/test/test_nlp_expr.jl
index 53b6704073e..9fc10703621 100644
--- a/test/test_nlp_expr.jl
+++ b/test/test_nlp_expr.jl
@@ -8,6 +8,8 @@ module TestNLPExpr
 using JuMP
 using Test
 
+import LinearAlgebra
+
 function test_extension_univariate_operators(
     ModelType = Model,
     VariableRefType = VariableRef,
@@ -828,4 +830,18 @@ function test_redefinition_of_function()
     return
 end
 
+function test_linear_algebra_errors()
+    model = Model()
+    @variable(model, x[1:2, 1:2])
+    @test_throws MOI.UnsupportedNonlinearOperator LinearAlgebra.det(x)
+    @test_throws MOI.UnsupportedNonlinearOperator LinearAlgebra.logdet(x)
+    @test_throws MOI.UnsupportedNonlinearOperator LinearAlgebra.norm(x)
+    @test_throws MOI.UnsupportedNonlinearOperator LinearAlgebra.nullspace(x)
+    @test_throws MOI.UnsupportedNonlinearOperator LinearAlgebra.qr(x)
+    y = 2.0 .* x[:, 2] .+ 1.0
+    @test_throws MOI.UnsupportedNonlinearOperator LinearAlgebra.norm(y)
+    @test_throws MOI.UnsupportedNonlinearOperator LinearAlgebra.nullspace(y)
+    return
+end
+
 end  # module