diff --git a/src/basic.jl b/src/basic.jl
index 4916651..aba657a 100644
--- a/src/basic.jl
+++ b/src/basic.jl
@@ -265,8 +265,6 @@ function applykraus(K, M)
 end
 export applykraus
 
-LA.I(dim::Integer, sp::Bool) = sp ? SA.sparse(LA.I(dim)) : LA.I(dim)
-
 function _orthonormal_range_svd!(
     A::AbstractMatrix{T};
     tol::Union{Real,Nothing} = nothing,
@@ -317,14 +315,11 @@ returns the actual projection `V * V'`.
 Reference: [Watrous' book](https://cs.uwaterloo.ca/~watrous/TQI/), Sec. 7.1.1
 """
 function symmetric_projection(::Type{T}, dim::Integer, n::Integer; partial::Bool = true) where {T}
-    if T <: SA.CHOLMOD.VTypes #sparse qr decomposition fails for anything other than Float64 or ComplexF64
-        P = SA.spzeros(T, dim^n, dim^n)
-    else
-        P = zeros(T, dim^n, dim^n)
-    end
+    is_sparse = T <: SA.CHOLMOD.VTypes #sparse qr decomposition fails for anything other than Float64 or ComplexF64
+    P = is_sparse ? SA.spzeros(T, dim^n, dim^n) : zeros(T, dim^n, dim^n)
     perms = Combinatorics.permutations(1:n)
     for perm in perms
-        P .+= permutation_matrix(dim, perm; sp = true)
+        P .+= permutation_matrix(dim, perm; is_sparse)
     end
     P ./= length(perms)
     if partial
diff --git a/src/multilinear.jl b/src/multilinear.jl
index cf25621..c89c7fe 100644
--- a/src/multilinear.jl
+++ b/src/multilinear.jl
@@ -292,9 +292,11 @@ If `dims` is an Integer, assumes there are `length(perm)` subsystems of equal di
 function permutation_matrix(
     dims::Union{Integer,AbstractVector{<:Integer}},
     perm::AbstractVector{<:Integer};
-    sp::Bool = true
+    is_sparse::Bool = true
 )
     dims = dims isa Integer ? fill(dims, length(perm)) : dims
-    permute_systems(LA.I(prod(dims), sp), perm, dims; rows_only = true)
+    d = prod(dims)
+    id = is_sparse ? SA.sparse(LA.I, (d, d)) : LA.I(d)
+    permute_systems(id, perm, dims; rows_only = true)
 end
 export permutation_matrix