diff --git a/CHANGELOG.md b/CHANGELOG.md
index f7e3606..cce4b47 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -13,6 +13,7 @@ This project adheres to [Semantic Versioning](http://semver.org/).
 - Constrained conversion functions for assisting in situations where type
   inference is difficult.
 - An `ElementWise` trait for non-mathematical element-wise operations.
+- A default implementation for `EuclideanVector::angle`.
 
 ### Changed
 
@@ -21,13 +22,16 @@ This project adheres to [Semantic Versioning](http://semver.org/).
   formatting.
 - Marks vectors, points, matrices, and angles as `#[repr(C, packed)]`.
 - Renames the `Vector::{length, length2}` functions to `Vector::{magnitude, magnitude2}`.
-- Moved `Angle::new` to be directly implemented on the `Rad` and `Deg` types.
+- Move `Angle::new` to be directly implemented on the `Rad` and `Deg` types.
+- Move `Vector::dot` to `EuclideanVector` trait.
+- Move `Vector::from_value` to `Array` trait.
 
 ### Removed
 
 - The non-mathematical operator trait implementations have been removed from
   the `Vector` trait, in favor of the `ElementWise` trait.
 - `Angle::equiv`.
+- Remove `neg_self` method on vectors and matrices.
 
 ## [v0.7.0] - 2015-12-23
 
diff --git a/src/array.rs b/src/array.rs
index f71c37f..df068de 100644
--- a/src/array.rs
+++ b/src/array.rs
@@ -26,6 +26,17 @@ pub trait Array where
 {
     type Element: Copy;
 
+    /// Construct a vector from a single value, replicating it.
+    ///
+    /// ```rust
+    /// use cgmath::prelude::*;
+    /// use cgmath::Vector3;
+    ///
+    /// assert_eq!(Vector3::from_value(1),
+    ///            Vector3::new(1, 1, 1));
+    /// ```
+    fn from_value(value: Self::Element) -> Self;
+
     /// Get the pointer to the first element of the array.
     #[inline]
     fn as_ptr(&self) -> *const Self::Element {
diff --git a/src/matrix.rs b/src/matrix.rs
index f364072..aa1aaf2 100644
--- a/src/matrix.rs
+++ b/src/matrix.rs
@@ -100,15 +100,6 @@ impl<S: BaseFloat> Matrix2<S> {
     }
 }
 
-impl<S: Copy + Neg<Output = S>> Matrix2<S> {
-    /// Negate this `Matrix2` in-place.
-    #[inline]
-    pub fn neg_self(&mut self) {
-        self[0].neg_self();
-        self[1].neg_self();
-    }
-}
-
 impl<S: BaseFloat> Matrix3<S> {
     /// Create a new matrix, providing values for each index.
     #[inline]
@@ -200,16 +191,6 @@ impl<S: BaseFloat> Matrix3<S> {
     }
 }
 
-impl<S: Copy + Neg<Output = S>> Matrix3<S> {
-    /// Negate this `Matrix3` in-place.
-    #[inline]
-    pub fn neg_self(&mut self) {
-        self[0].neg_self();
-        self[1].neg_self();
-        self[2].neg_self();
-    }
-}
-
 impl<S: BaseFloat> Matrix4<S> {
     /// Create a new matrix, providing values for each index.
     #[inline]
@@ -267,17 +248,6 @@ impl<S: BaseFloat> Matrix4<S> {
     }
 }
 
-impl<S: Copy + Neg<Output = S>> Matrix4<S> {
-    /// Negate this `Matrix4` in-place.
-    #[inline]
-    pub fn neg_self(&mut self) {
-        self[0].neg_self();
-        self[1].neg_self();
-        self[2].neg_self();
-        self[3].neg_self();
-    }
-}
-
 /// A column-major matrix of arbitrary dimensions.
 pub trait Matrix  where
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
diff --git a/src/point.rs b/src/point.rs
index fbf21fd..e35877c 100644
--- a/src/point.rs
+++ b/src/point.rs
@@ -169,10 +169,30 @@ macro_rules! impl_point {
         impl<S: BaseNum> Array for $PointN<S> {
             type Element = S;
 
-            #[inline] fn sum(self) -> S { fold_array!(add, { $(self.$field),+ }) }
-            #[inline] fn product(self) -> S { fold_array!(mul, { $(self.$field),+ }) }
-            #[inline] fn min(self) -> S { fold_array!(partial_min, { $(self.$field),+ }) }
-            #[inline] fn max(self) -> S { fold_array!(partial_max, { $(self.$field),+ }) }
+            #[inline]
+            fn from_value(scalar: S) -> $PointN<S> {
+                $PointN { $($field: scalar),+ }
+            }
+
+            #[inline]
+            fn sum(self) -> S where S: Add<Output = S> {
+                fold_array!(add, { $(self.$field),+ })
+            }
+
+            #[inline]
+            fn product(self) -> S where S: Mul<Output = S> {
+                fold_array!(mul, { $(self.$field),+ })
+            }
+
+            #[inline]
+            fn min(self) -> S where S: PartialOrd {
+                fold_array!(partial_min, { $(self.$field),+ })
+            }
+
+            #[inline]
+            fn max(self) -> S where S: PartialOrd {
+                fold_array!(partial_max, { $(self.$field),+ })
+            }
         }
 
         impl<S: BaseNum> Point for $PointN<S> {
diff --git a/src/rotation.rs b/src/rotation.rs
index 993188e..614a5ac 100644
--- a/src/rotation.rs
+++ b/src/rotation.rs
@@ -22,7 +22,7 @@ use matrix::{Matrix2, Matrix3};
 use num::BaseFloat;
 use point::{Point, Point2, Point3};
 use quaternion::Quaternion;
-use vector::{Vector, Vector2, Vector3};
+use vector::{EuclideanVector, Vector2, Vector3};
 
 /// A trait for a generic rotation. A rotation is a transformation that
 /// creates a circular motion, and preserves at least one point in the space.
diff --git a/src/vector.rs b/src/vector.rs
index 47decd2..659527f 100644
--- a/src/vector.rs
+++ b/src/vector.rs
@@ -22,11 +22,10 @@
 //! vector are also provided:
 //!
 //! ```rust
-//! use cgmath::{Vector, Vector2, Vector3, Vector4, vec2, vec3};
+//! use cgmath::{Vector, Vector2, Vector3, Vector4, vec3};
 //!
 //! assert_eq!(Vector2::new(1.0f64, 0.0f64), Vector2::unit_x());
 //! assert_eq!(vec3(0.0f64, 0.0f64, 0.0f64), Vector3::zero());
-//! assert_eq!(Vector2::from_value(1.0f64), vec2(1.0, 1.0));
 //! ```
 //!
 //! Vectors can be manipulated with typical mathematical operations (addition,
@@ -62,7 +61,8 @@
 //! and [cross products](http://en.wikipedia.org/wiki/Cross_product).
 //!
 //! ```rust
-//! use cgmath::{Vector, Vector2, Vector3, Vector4, dot};
+//! use cgmath::{Vector, EuclideanVector};
+//! use cgmath::{Vector2, Vector3, Vector4};
 //!
 //! // All vectors implement the dot product as a method:
 //! let a: Vector2<f64> = Vector2::new(3.0, 6.0);
@@ -70,7 +70,7 @@
 //! assert_eq!(a.dot(b), 0.0);
 //!
 //! // But there is also a top-level function:
-//! assert_eq!(a.dot(b), dot(a, b));
+//! assert_eq!(a.dot(b), cgmath::dot(a, b));
 //!
 //! // Cross products are defined for 3-dimensional vectors:
 //! let e: Vector3<f64> = Vector3::unit_x();
@@ -100,7 +100,49 @@ use approx::ApproxEq;
 use array::{Array, ElementWise};
 use num::{BaseNum, BaseFloat, PartialOrd};
 
-/// A trait that specifies a range of numeric operations for vectors.
+/// Vectors that can be [added](http://mathworld.wolfram.com/VectorAddition.html)
+/// together and [multiplied](https://en.wikipedia.org/wiki/Scalar_multiplication)
+/// by scalars.
+///
+/// # Required operators
+///
+/// ## Vector addition
+///
+/// Vectors can be added, subtracted, or negated via the following traits:
+///
+/// - `Add<Output = Self>`
+/// - `Sub<Output = Self>`
+/// - `Neg<Output = Self>`
+///
+/// ```rust
+/// use cgmath::Vector3;
+///
+/// let velocity0 = Vector3::new(1, 2, 0);
+/// let velocity1 = Vector3::new(1, 1, 0);
+///
+/// let total_velocity = velocity0 + velocity1;
+/// let velocity_diff = velocity1 - velocity0;
+/// let reversed_velocity0 = -velocity0;
+/// ```
+///
+/// ## Scalar multiplication
+///
+/// Vectors can be multiplied or divided by their associated scalars via the
+/// following traits:
+///
+/// - `Mul<Self::Scalar, Output = Self>`
+/// - `Div<Self::Scalar, Output = Self>`
+/// - `Rem<Self::Scalar, Output = Self>`
+///
+/// ```rust
+/// use cgmath::Vector2;
+///
+/// let translation = Vector2::new(3.0, 4.0);
+/// let scale_factor = 2.0;
+///
+/// let upscaled_translation = translation * scale_factor;
+/// let downscaled_translation = translation / scale_factor;
+/// ```
 pub trait Vector: Copy + Clone where
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
     Self: Array<Element = <Self as Vector>::Scalar>,
@@ -115,27 +157,29 @@ pub trait Vector: Copy + Clone where
     /// The associated scalar.
     type Scalar: BaseNum;
 
-    /// Construct a vector from a single value, replicating it.
-    fn from_value(scalar: Self::Scalar) -> Self;
-
-    /// The additive identity vector. Adding this vector with another has no effect.
-    #[inline]
-    fn zero() -> Self { Self::from_value(Self::Scalar::zero()) }
-
-    /// Vector dot product
-    fn dot(self, other: Self) -> Self::Scalar;
+    /// The additive identity.
+    ///
+    /// Adding this to another `Self` value has no effect.
+    ///
+    /// ```rust
+    /// use cgmath::prelude::*;
+    /// use cgmath::Vector2;
+    ///
+    /// let v = Vector2::new(1, 2);
+    /// assert_eq!(v + Vector2::zero(), v);
+    /// ```
+    fn zero() -> Self;
 }
 
-/// Dot product of two vectors.
-#[inline] pub fn dot<V: Vector>(a: V, b: V) -> V::Scalar { V::dot(a, b) }
-
 /// A 2-dimensional vector.
 ///
 /// This type is marked as `#[repr(C, packed)]`.
 #[repr(C, packed)]
 #[derive(PartialEq, Eq, Copy, Clone, Hash, RustcEncodable, RustcDecodable)]
 pub struct Vector2<S> {
+    /// The x component of the vector.
     pub x: S,
+    /// The y component of the vector.
     pub y: S,
 }
 
@@ -145,8 +189,11 @@ pub struct Vector2<S> {
 #[repr(C, packed)]
 #[derive(PartialEq, Eq, Copy, Clone, Hash, RustcEncodable, RustcDecodable)]
 pub struct Vector3<S> {
+    /// The x component of the vector.
     pub x: S,
+    /// The y component of the vector.
     pub y: S,
+    /// The z component of the vector.
     pub z: S,
 }
 
@@ -156,9 +203,13 @@ pub struct Vector3<S> {
 #[repr(C, packed)]
 #[derive(PartialEq, Eq, Copy, Clone, Hash, RustcEncodable, RustcDecodable)]
 pub struct Vector4<S> {
+    /// The x component of the vector.
     pub x: S,
+    /// The y component of the vector.
     pub y: S,
+    /// The z component of the vector.
     pub z: S,
+    /// The w component of the vector.
     pub w: S,
 }
 
@@ -173,14 +224,6 @@ macro_rules! impl_vector {
             }
         }
 
-        impl<$S: Copy + Neg<Output = $S>> $VectorN<$S> {
-            /// Negate this vector in-place (multiply by -1).
-            #[inline]
-            pub fn neg_self(&mut self) {
-                $(self.$field = -self.$field);+
-            }
-        }
-
         /// The short constructor.
         #[inline]
         pub fn $constructor<S>($($field: S),+) -> $VectorN<S> {
@@ -198,18 +241,39 @@ macro_rules! impl_vector {
         impl<S: Copy> Array for $VectorN<S> {
             type Element = S;
 
-            #[inline] fn sum(self) -> S where S: Add<Output = S> { fold_array!(add, { $(self.$field),+ }) }
-            #[inline] fn product(self) -> S where S: Mul<Output = S> { fold_array!(mul, { $(self.$field),+ }) }
-            #[inline] fn min(self) -> S where S: PartialOrd { fold_array!(partial_min, { $(self.$field),+ }) }
-            #[inline] fn max(self) -> S where S: PartialOrd { fold_array!(partial_max, { $(self.$field),+ }) }
+            #[inline]
+            fn from_value(scalar: S) -> $VectorN<S> {
+                $VectorN { $($field: scalar),+ }
+            }
+
+            #[inline]
+            fn sum(self) -> S where S: Add<Output = S> {
+                fold_array!(add, { $(self.$field),+ })
+            }
+
+            #[inline]
+            fn product(self) -> S where S: Mul<Output = S> {
+                fold_array!(mul, { $(self.$field),+ })
+            }
+
+            #[inline]
+            fn min(self) -> S where S: PartialOrd {
+                fold_array!(partial_min, { $(self.$field),+ })
+            }
+
+            #[inline]
+            fn max(self) -> S where S: PartialOrd {
+                fold_array!(partial_max, { $(self.$field),+ })
+            }
         }
 
         impl<S: BaseNum> Vector for $VectorN<S> {
             type Scalar = S;
 
-            #[inline] fn from_value(scalar: S) -> $VectorN<S> { $VectorN { $($field: scalar),+ } }
-
-            #[inline] fn dot(self, other: $VectorN<S>) -> S { $VectorN::mul_element_wise(self, other).sum() }
+            #[inline]
+            fn zero() -> Self {
+                Self::from_value(Self::Scalar::zero())
+            }
         }
 
         impl<S: Neg<Output = S>> Neg for $VectorN<S> {
@@ -461,13 +525,19 @@ impl<S: BaseNum> Vector4<S> {
     }
 }
 
-/// Specifies geometric operations for vectors. This is only implemented for
-/// vectors of float types.
+/// Vectors that also have a [dot](https://en.wikipedia.org/wiki/Dot_product)
+/// (or [inner](https://en.wikipedia.org/wiki/Inner_product_space)) product.
+///
+/// The dot product allows for the definition of other useful operations, like
+/// finding the magnitude of a vector or normalizing it.
 pub trait EuclideanVector: Vector + Sized where
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
     <Self as Vector>::Scalar: BaseFloat,
     Self: ApproxEq<Epsilon = <Self as Vector>::Scalar>,
 {
+    /// Vector dot (or inner) product.
+    fn dot(self, other: Self) -> Self::Scalar;
+
     /// Returns `true` if the vector is perpendicular (at right angles) to the
     /// other vector.
     fn is_perpendicular(self, other: Self) -> bool {
@@ -493,8 +563,10 @@ pub trait EuclideanVector: Vector + Sized where
         Float::sqrt(self.magnitude2())
     }
 
-    /// The angle between the vector and `other`, in radians.
-    fn angle(self, other: Self) -> Rad<Self::Scalar>;
+    /// Returns the angle between two vectors in radians.
+    fn angle(self, other: Self) -> Rad<Self::Scalar> {
+        Rad::acos(Self::dot(self, other) / (self.magnitude() * other.magnitude()))
+    }
 
     /// Returns a vector with the same direction, but with a magnitude of `1`.
     #[inline]
@@ -519,7 +591,20 @@ pub trait EuclideanVector: Vector + Sized where
     }
 }
 
+/// Dot product of two vectors.
+#[inline]
+pub fn dot<V: EuclideanVector>(a: V, b: V) -> V::Scalar where
+    V::Scalar: BaseFloat,
+{
+    V::dot(a, b)
+}
+
 impl<S: BaseFloat> EuclideanVector for Vector2<S> {
+    #[inline]
+    fn dot(self, other: Vector2<S>) -> S {
+        Vector2::mul_element_wise(self, other).sum()
+    }
+
     #[inline]
     fn angle(self, other: Vector2<S>) -> Rad<S> {
         Rad::atan2(Self::perp_dot(self, other), Self::dot(self, other))
@@ -527,6 +612,11 @@ impl<S: BaseFloat> EuclideanVector for Vector2<S> {
 }
 
 impl<S: BaseFloat> EuclideanVector for Vector3<S> {
+    #[inline]
+    fn dot(self, other: Vector3<S>) -> S {
+        Vector3::mul_element_wise(self, other).sum()
+    }
+
     #[inline]
     fn angle(self, other: Vector3<S>) -> Rad<S> {
         Rad::atan2(self.cross(other).magnitude(), Self::dot(self, other))
@@ -535,8 +625,8 @@ impl<S: BaseFloat> EuclideanVector for Vector3<S> {
 
 impl<S: BaseFloat> EuclideanVector for Vector4<S> {
     #[inline]
-    fn angle(self, other: Vector4<S>) -> Rad<S> {
-        Rad::acos(Self::dot(self, other) / (self.magnitude() * other.magnitude()))
+    fn dot(self, other: Vector4<S>) -> S {
+        Vector4::mul_element_wise(self, other).sum()
     }
 }
 
diff --git a/tests/vector.rs b/tests/vector.rs
index c8d84f7..d7ed20b 100644
--- a/tests/vector.rs
+++ b/tests/vector.rs
@@ -122,9 +122,9 @@ fn test_rem() {
 
 #[test]
 fn test_dot() {
-    assert_eq!(Vector2::new(1isize, 2isize).dot(Vector2::new(3isize, 4isize)), 11isize);
-    assert_eq!(Vector3::new(1isize, 2isize, 3isize).dot(Vector3::new(4isize, 5isize, 6isize)), 32isize);
-    assert_eq!(Vector4::new(1isize, 2isize, 3isize, 4isize).dot(Vector4::new(5isize, 6isize, 7isize, 8isize)), 70isize);
+    assert_eq!(Vector2::new(1.0, 2.0).dot(Vector2::new(3.0, 4.0)), 11.0);
+    assert_eq!(Vector3::new(1.0, 2.0, 3.0).dot(Vector3::new(4.0, 5.0, 6.0)), 32.0);
+    assert_eq!(Vector4::new(1.0, 2.0, 3.0, 4.0).dot(Vector4::new(5.0, 6.0, 7.0, 8.0)), 70.0);
 }
 
 #[test]