diff --git a/src/assert.rs b/src/assert.rs
index 880dba1b..da9d6ffa 100644
--- a/src/assert.rs
+++ b/src/assert.rs
@@ -1,23 +1,21 @@
 //! Assertions for array
 
-use std::iter::Sum;
-use num_traits::Float;
 use ndarray::*;
 
 use super::types::*;
-use super::vector::*;
+use super::norm::*;
 
 pub fn rclose<A, Tol>(test: A, truth: A, rtol: Tol) -> Result<Tol, Tol>
-    where A: LinalgScalar + Absolute<Output = Tol>,
-          Tol: Float
+    where A: Field + Absolute<Output = Tol>,
+          Tol: RealField
 {
     let dev = (test - truth).abs() / truth.abs();
     if dev < rtol { Ok(dev) } else { Err(dev) }
 }
 
 pub fn aclose<A, Tol>(test: A, truth: A, atol: Tol) -> Result<Tol, Tol>
-    where A: LinalgScalar + Absolute<Output = Tol>,
-          Tol: Float
+    where A: Field + Absolute<Output = Tol>,
+          Tol: RealField
 {
     let dev = (test - truth).abs();
     if dev < atol { Ok(dev) } else { Err(dev) }
@@ -25,8 +23,8 @@ pub fn aclose<A, Tol>(test: A, truth: A, atol: Tol) -> Result<Tol, Tol>
 
 /// check two arrays are close in maximum norm
 pub fn close_max<A, Tol, S1, S2, D>(test: &ArrayBase<S1, D>, truth: &ArrayBase<S2, D>, atol: Tol) -> Result<Tol, Tol>
-    where A: LinalgScalar + Absolute<Output = Tol>,
-          Tol: Float + Sum,
+    where A: Field + Absolute<Output = Tol>,
+          Tol: RealField,
           S1: Data<Elem = A>,
           S2: Data<Elem = A>,
           D: Dimension
@@ -37,8 +35,8 @@ pub fn close_max<A, Tol, S1, S2, D>(test: &ArrayBase<S1, D>, truth: &ArrayBase<S
 
 /// check two arrays are close in L1 norm
 pub fn close_l1<A, Tol, S1, S2, D>(test: &ArrayBase<S1, D>, truth: &ArrayBase<S2, D>, rtol: Tol) -> Result<Tol, Tol>
-    where A: LinalgScalar + Absolute<Output = Tol>,
-          Tol: Float + Sum,
+    where A: Field + Absolute<Output = Tol>,
+          Tol: RealField,
           S1: Data<Elem = A>,
           S2: Data<Elem = A>,
           D: Dimension
@@ -49,8 +47,8 @@ pub fn close_l1<A, Tol, S1, S2, D>(test: &ArrayBase<S1, D>, truth: &ArrayBase<S2
 
 /// check two arrays are close in L2 norm
 pub fn close_l2<A, Tol, S1, S2, D>(test: &ArrayBase<S1, D>, truth: &ArrayBase<S2, D>, rtol: Tol) -> Result<Tol, Tol>
-    where A: LinalgScalar + Absolute<Output = Tol>,
-          Tol: Float + Sum,
+    where A: Field + Absolute<Output = Tol>,
+          Tol: RealField,
           S1: Data<Elem = A>,
           S2: Data<Elem = A>,
           D: Dimension
diff --git a/src/impl2/mod.rs b/src/impl2/mod.rs
index 91b0bcf0..fd5dba5e 100644
--- a/src/impl2/mod.rs
+++ b/src/impl2/mod.rs
@@ -15,8 +15,12 @@ pub use self::eigh::*;
 
 use super::error::*;
 
-pub trait LapackScalar: OperatorNorm_ + QR_ + SVD_ + Solve_ + Cholesky_ + Eigh_ {}
-impl<A> LapackScalar for A where A: OperatorNorm_ + QR_ + SVD_ + Solve_ + Cholesky_ + Eigh_ {}
+trait_alias!(LapackScalar: OperatorNorm_,
+             QR_,
+             SVD_,
+             Solve_,
+             Cholesky_,
+             Eigh_);
 
 pub fn into_result<T>(info: i32, val: T) -> Result<T> {
     if info == 0 {
diff --git a/src/lib.rs b/src/lib.rs
index b45c369b..f654d8a9 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -43,6 +43,7 @@ extern crate enum_error_derive;
 #[macro_use]
 extern crate derive_new;
 
+#[macro_use]
 pub mod types;
 pub mod error;
 pub mod layout;
@@ -56,12 +57,12 @@ pub mod solve;
 pub mod cholesky;
 pub mod eigh;
 
-pub mod vector;
 pub mod matrix;
 pub mod square;
 pub mod triangular;
 
-pub mod util;
 pub mod generate;
 pub mod assert;
+pub mod norm;
+
 pub mod prelude;
diff --git a/src/vector.rs b/src/norm.rs
similarity index 62%
rename from src/vector.rs
rename to src/norm.rs
index e770e7ed..63877b07 100644
--- a/src/vector.rs
+++ b/src/norm.rs
@@ -1,8 +1,7 @@
 //! Define trait for vectors
 
-use std::iter::Sum;
+use std::ops::*;
 use ndarray::*;
-use num_traits::Float;
 
 use super::types::*;
 
@@ -24,8 +23,8 @@ pub trait Norm {
 }
 
 impl<A, S, D, T> Norm for ArrayBase<S, D>
-    where A: LinalgScalar + Absolute<Output = T>,
-          T: Float + Sum,
+    where A: Field + Absolute<Output = T>,
+          T: RealField,
           S: Data<Elem = A>,
           D: Dimension
 {
@@ -43,3 +42,23 @@ impl<A, S, D, T> Norm for ArrayBase<S, D>
         })
     }
 }
+
+pub enum NormalizeAxis {
+    Row = 0,
+    Column = 1,
+}
+
+/// normalize in L2 norm
+pub fn normalize<A, S, T>(mut m: ArrayBase<S, Ix2>, axis: NormalizeAxis) -> (ArrayBase<S, Ix2>, Vec<T>)
+    where A: Field + Absolute<Output = T> + Div<T, Output = A>,
+          S: DataMut<Elem = A>,
+          T: RealField
+{
+    let mut ms = Vec::new();
+    for mut v in m.axis_iter_mut(Axis(axis as usize)) {
+        let n = v.norm();
+        ms.push(n);
+        v.map_inplace(|x| *x = *x / n)
+    }
+    (m, ms)
+}
diff --git a/src/prelude.rs b/src/prelude.rs
index d3f0da73..f34cb921 100644
--- a/src/prelude.rs
+++ b/src/prelude.rs
@@ -1,8 +1,7 @@
-pub use vector::Norm;
 pub use matrix::Matrix;
 pub use square::SquareMatrix;
 pub use triangular::*;
-pub use util::*;
+pub use norm::*;
 pub use types::*;
 pub use generate::*;
 pub use assert::*;
diff --git a/src/types.rs b/src/types.rs
index d8118b69..d2ce0759 100644
--- a/src/types.rs
+++ b/src/types.rs
@@ -1,11 +1,39 @@
 
-pub use num_complex::Complex32 as c32;
-pub use num_complex::Complex64 as c64;
-use num_complex::Complex;
-use num_traits::Float;
 use std::ops::*;
+use std::fmt::Debug;
+use std::iter::Sum;
+use num_complex::Complex;
+use num_traits::*;
 use rand::Rng;
 use rand::distributions::*;
+use ndarray::LinalgScalar;
+
+use super::impl2::LapackScalar;
+
+pub use num_complex::Complex32 as c32;
+pub use num_complex::Complex64 as c64;
+
+macro_rules! trait_alias {
+    ($name:ident: $($t:ident),*) => {
+
+pub trait $name : $($t +)* {}
+
+impl<T> $name for T where T: $($t +)* {}
+
+}} // trait_alias!
+
+trait_alias!(Field: LapackScalar,
+             LinalgScalar,
+             AssociatedReal,
+             AssociatedComplex,
+             Absolute,
+             SquareRoot,
+             Conjugate,
+             RandNormal,
+             Sum,
+             Debug);
+
+trait_alias!(RealField: Field, Float);
 
 pub trait AssociatedReal: Sized {
     type Real: Float + Mul<Self, Output = Self>;
@@ -16,13 +44,17 @@ pub trait AssociatedComplex: Sized {
 
 /// Field with norm
 pub trait Absolute {
-    type Output: Float;
+    type Output: RealField;
     fn squared(&self) -> Self::Output;
     fn abs(&self) -> Self::Output {
         self.squared().sqrt()
     }
 }
 
+pub trait SquareRoot {
+    fn sqrt(&self) -> Self;
+}
+
 pub trait Conjugate: Copy {
     fn conj(self) -> Self;
 }
@@ -70,6 +102,18 @@ impl Absolute for $complex {
     }
 }
 
+impl SquareRoot for $real {
+    fn sqrt(&self) -> Self {
+        Float::sqrt(*self)
+    }
+}
+
+impl SquareRoot for $complex {
+    fn sqrt(&self) -> Self {
+        Complex::sqrt(self)
+    }
+}
+
 impl Conjugate for $real {
     fn conj(self) -> Self {
         self
diff --git a/src/util.rs b/src/util.rs
deleted file mode 100644
index 03cb9482..00000000
--- a/src/util.rs
+++ /dev/null
@@ -1,29 +0,0 @@
-//! misc utilities
-
-use std::iter::Sum;
-use ndarray::*;
-use num_traits::Float;
-use std::ops::Div;
-
-use super::types::*;
-use super::vector::*;
-
-pub enum NormalizeAxis {
-    Row = 0,
-    Column = 1,
-}
-
-/// normalize in L2 norm
-pub fn normalize<A, S, T>(mut m: ArrayBase<S, Ix2>, axis: NormalizeAxis) -> (ArrayBase<S, Ix2>, Vec<T>)
-    where A: LinalgScalar + Absolute<Output = T> + Div<T, Output = A>,
-          S: DataMut<Elem = A>,
-          T: Float + Sum
-{
-    let mut ms = Vec::new();
-    for mut v in m.axis_iter_mut(Axis(axis as usize)) {
-        let n = v.norm();
-        ms.push(n);
-        v.map_inplace(|x| *x = *x / n)
-    }
-    (m, ms)
-}