Add simple example on how to compute Cholesky decomposition.

doc/C06_TutorialLinearAlgebra.dox

@@ -144,6 +144,9 @@ You need an eigendecomposition here, see available such decompositions on \ref T
 Make sure to check if your matrix is self-adjoint, as is often the case in these problems. Here's an example using
 SelfAdjointEigenSolver, it could easily be adapted to general matrices using EigenSolver or ComplexEigenSolver.
 
+The computation of eigenvalues and eigenvectors does not necessarily converge, but such failure to converge is
+very rare. The call to info() is to check for this possibility.
+
 <table class="example">
 <tr><th>Example:</th><th>Output:</th></tr>
 <tr>

doc/snippets/LLT_example.cpp

@@ -0,0 +1,12 @@
+MatrixXd A(3,3);
+A << 4,-1,2, -1,6,0, 2,0,5;
+cout << "The matrix A is" << endl << A << endl;
+
+LLT<MatrixXd> lltOfA(A); // compute the Cholesky decomposition of A
+MatrixXd L = lltOfA.matrixL(); // retrieve factor L  in the decomposition
+// The previous two lines can also be written as "L = A.llt().matrixL()"
+
+cout << "The Cholesky factor L is" << endl << L << endl;
+cout << "To check this, let us compute L * L.transpose()" << endl;
+cout << L * L.transpose() << endl;
+cout << "This should equal the matrix A" << endl;