Added more detailed docs to the QR decompositions classes.

3 files changed, 21 insertions, 4 deletions

diff --git a/Eigen/src/QR/ColPivHouseholderQR.h b/Eigen/src/QR/ColPivHouseholderQR.h
index cab13ff0d..f34658fa9 100644
--- a/Eigen/src/QR/ColPivHouseholderQR.h
+++ b/Eigen/src/QR/ColPivHouseholderQR.h
@@ -34,7 +34,13 @@
   *
   * \param MatrixType the type of the matrix of which we are computing the QR decomposition
   *
-  * This class performs a rank-revealing QR decomposition using Householder transformations.
+  * This class performs a rank-revealing QR decomposition of a matrix \b A into matrices \b P, \b Q and \b R
+  * such that 
+  * \f[
+  *  \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \mathbf{R}
+  * \f]
+  * by using Householder transformations. Here, \b P is a permutation matrix, \b Q a unitary matrix and \b R an 
+  * upper triangular matrix.
   *
   * This decomposition performs column pivoting in order to be rank-revealing and improve
   * numerical stability. It is slower than HouseholderQR, and faster than FullPivHouseholderQR.
diff --git a/Eigen/src/QR/FullPivHouseholderQR.h b/Eigen/src/QR/FullPivHouseholderQR.h
index 201d63128..e228aeb44 100644
--- a/Eigen/src/QR/FullPivHouseholderQR.h
+++ b/Eigen/src/QR/FullPivHouseholderQR.h
@@ -34,7 +34,13 @@
   *
   * \param MatrixType the type of the matrix of which we are computing the QR decomposition
   *
-  * This class performs a rank-revealing QR decomposition using Householder transformations.
+  * This class performs a rank-revealing QR decomposition of a matrix \b A into matrices \b P, \b Q and \b R
+  * such that 
+  * \f[
+  *  \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \mathbf{R}
+  * \f]
+  * by using Householder transformations. Here, \b P is a permutation matrix, \b Q a unitary matrix and \b R an 
+  * upper triangular matrix.
   *
   * This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal
   * numerical stability. The trade-off is that it is slower than HouseholderQR and ColPivHouseholderQR.
diff --git a/Eigen/src/QR/HouseholderQR.h b/Eigen/src/QR/HouseholderQR.h
index fe316d2ee..f8d759772 100644
--- a/Eigen/src/QR/HouseholderQR.h
+++ b/Eigen/src/QR/HouseholderQR.h
@@ -36,8 +36,13 @@
   *
   * \param MatrixType the type of the matrix of which we are computing the QR decomposition
   *
-  * This class performs a QR decomposition using Householder transformations. The result is
-  * stored in a compact way compatible with LAPACK.
+  * This class performs a QR decomposition of a matrix \b A into matrices \b Q and \b R
+  * such that 
+  * \f[
+  *  \mathbf{A} = \mathbf{Q} \, \mathbf{R}
+  * \f]
+  * by using Householder transformations. Here, \b Q a unitary matrix and \b R an upper triangular matrix.
+  * The result is stored in a compact way compatible with LAPACK.
   *
   * Note that no pivoting is performed. This is \b not a rank-revealing decomposition.
   * If you want that feature, use FullPivHouseholderQR or ColPivHouseholderQR instead.