diff --git a/Project.toml b/Project.toml
index 224b4b5..25f1f8c 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "FusionTensors"
 uuid = "e16ca583-1f51-4df0-8e12-57d32947d33e"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.5.9"
+version = "0.5.10"
 
 [deps]
 Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
diff --git a/src/fusiontensor/linear_algebra_interface.jl b/src/fusiontensor/linear_algebra_interface.jl
index b63bc03..2d2a7ca 100644
--- a/src/fusiontensor/linear_algebra_interface.jl
+++ b/src/fusiontensor/linear_algebra_interface.jl
@@ -33,13 +33,20 @@ function LinearAlgebra.mul!(
   return C
 end
 
-function LinearAlgebra.norm(ft::FusionTensor)
+function LinearAlgebra.norm(ft::FusionTensor, p::Real=2)
   m = data_matrix(ft)
   row_sectors = sectors(codomain_axis(ft))
-  n2 = sum(eachblockstoredindex(m); init=zero(real(eltype(ft)))) do b
-    return quantum_dimension(row_sectors[Int(first(Tuple(b)))]) * norm(m[b])^2
+  np = sum(eachblockstoredindex(m); init=zero(real(eltype(ft)))) do b
+    return quantum_dimension(row_sectors[Int(first(Tuple(b)))]) * norm(m[b], p)^p
   end
-  return sqrt(n2)
+  return np^(1 / p)
+end
+
+LinearAlgebra.normalize(ft::FusionTensor, p::Real=2) = ft / norm(ft, p)
+
+function LinearAlgebra.normalize!(ft::FusionTensor, p::Real=2)
+  data_matrix(ft) ./= norm(ft, p)
+  return ft
 end
 
 function LinearAlgebra.tr(ft::FusionTensor)
@@ -49,18 +56,3 @@ function LinearAlgebra.tr(ft::FusionTensor)
     return quantum_dimension(row_sectors[Int(first(Tuple(b)))]) * tr(m[b])
   end
 end
-
-function LinearAlgebra.qr(ft::FusionTensor)
-  qmat, rmat = block_qr(data_matrix(ft))
-  qtens = FusionTensor(qmat, codomain_axes(ft), (axes(qmat, 2),))
-  rtens = FusionTensor(rmat, (axes(rmat, 1),), domain_axes(ft))
-  return qtens, rtens
-end
-
-function LinearAlgebra.svd(ft::FusionTensor)
-  umat, s, vmat = block_svd(data_matrix(ft))
-  utens = FusionTensor(umat, codomain_axes(ft), (axes(umat, 2),))
-  stens = FusionTensor(s, (axes(umat, 1),), (axes(vmat, 2),))
-  vtens = FusionTensor(vmat, (axes(vmat, 1),), domain_axes(ft))
-  return utens, stens, vtens
-end
diff --git a/test/test_linear_algebra.jl b/test/test_linear_algebra.jl
index 669457f..9b9f66c 100644
--- a/test/test_linear_algebra.jl
+++ b/test/test_linear_algebra.jl
@@ -1,11 +1,11 @@
-using LinearAlgebra: norm, tr
+using LinearAlgebra: norm, normalize, normalize!, tr
 using Test: @test, @testset
 
 using BlockArrays: BlockArrays
 
 using BlockSparseArrays: BlockSparseArrays
 using FusionTensors: FusionTensor, to_fusiontensor
-using GradedArrays: SU2, TrivialSector, U1, dual, gradedrange
+using GradedArrays: O2, SU2, TrivialSector, U1, dual, gradedrange
 
 include("setup.jl")
 
@@ -20,12 +20,31 @@ include("setup.jl")
 
   g0 = gradedrange([TrivialSector() => 2])
   gu1 = gradedrange([U1(1) => 1, U1(-1) => 1])
+  go2 = gradedrange([O2(1 / 2) => 1])
   gsu2 = gradedrange([SU2(1 / 2) => 1])
 
-  for g in [g0, gu1, gsu2]
+  for g in [g0, gu1, go2, gsu2]
     ft = to_fusiontensor(sdst, (g, g), (dual(g), dual(g)))
     @test isnothing(check_sanity(ft))
     @test norm(ft) ≈ √3 / 2
+    @test norm(ft, 2) ≈ √3 / 2
+    @test norm(ft, 2.0) ≈ √3 / 2
     @test isapprox(tr(ft), 0; atol=eps(Float64))
+
+    ft2 = normalize(ft)
+    @test norm(ft2) ≈ 1.0
+    @test norm(ft) ≈ √3 / 2  # unaffected by normalize
+    @test ft ≈ √3 / 2 * ft2
+    normalize!(ft)
+    @test norm(ft) ≈ 1.0
+  end
+
+  for g in [g0, gu1]
+    ft = to_fusiontensor(sdst, (g, g), (dual(g), dual(g)))
+    @test norm(ft, 1) ≈ 2.0
+  end
+  for g in [go2, gsu2]
+    ft = to_fusiontensor(sdst, (g, g), (dual(g), dual(g)))
+    @test norm(ft, 1) ≈ 1.5
   end
 end