* it's \returns not \Returns

* add some explanations in the typedefs page
* expand a bit the new QuickStartGuide. Some placeholders (not a pb since
it's not even yet linked to from other pages). The point I want to make is
that it's super important to have fully compilable short programs (even
with compile instructions for the first one) not just small snippets, at
least at the beginning. Let's start with examples of compilable programs.

Eigen/src/Core/Matrix.h

@@ -373,8 +373,20 @@ class Matrix : public MatrixBase<Matrix<_Scalar, _Rows, _Cols, _MaxRows, _MaxCol
 };
 
 /** \defgroup matrixtypedefs Global matrix typedefs
-  * Eigen defines several typedef shortcuts for most common matrix types.
-  * Here is the explicit list.
+  *
+  * Eigen defines several typedef shortcuts for most common matrix and vector types.
+  *
+  * The general patterns are the following:
+  *
+  * \c MatrixSizeType where \c Size can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
+  * and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
+  * for complex double.
+  *
+  * For example, \c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \c MatrixXf is a dynamic-size matrix of floats.
+  *
+  * There are also \c VectorSizeType and \c RowVectorSizeType which are self-explanatory. For example, \c Vector4cf is
+  * a fixed-size vector of 4 complex floats.
+  *
   * \sa class Matrix
   */
 

Eigen/src/Geometry/AngleAxis.h

@@ -104,7 +104,7 @@ public:
   operator* (const Matrix3& a, const AngleAxis& b)
   { return a * b.toRotationMatrix(); }
 
-  /** \Returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */
+  /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */
   AngleAxis inverse() const
   { return AngleAxis(-m_angle, m_axis); }
 

Eigen/src/Geometry/OrthoMethods.h

@@ -93,7 +93,7 @@ struct ei_someOrthogonal_selector<Derived,2>
   { return VectorType(-ei_conj(src.y()), ei_conj(src.x())).normalized(); }
 };
 
-/** \Returns an orthogonal vector of \c *this
+/** \returns an orthogonal vector of \c *this
   *
   * The size of \c *this must be at least 2. If the size is exactly 2,
   * then the returned vector is a counter clock wise rotation of \c *this, \ie (-y,x).

Eigen/src/Geometry/Rotation.h

@@ -138,10 +138,10 @@ public:
   /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
   inline Rotation2D(Scalar a) : m_angle(a) {}
 
-  /** \Returns the rotation angle */
+  /** \returns the rotation angle */
   inline Scalar angle() const { return m_angle; }
 
-  /** \Returns a read-write reference to the rotation angle */
+  /** \returns a read-write reference to the rotation angle */
   inline Scalar& angle() { return m_angle; }
 
   /** Automatic convertion to a 2D rotation matrix.
@@ -149,7 +149,7 @@ public:
     */
   inline operator Matrix2() const { return toRotationMatrix(); }
 
-  /** \Returns the inverse rotation */
+  /** \returns the inverse rotation */
   inline Rotation2D inverse() const { return -m_angle; }
 
   /** Concatenates two rotations */