fix various typos

doc/PreprocessorDirectives.dox

@@ -104,7 +104,7 @@ run time. However, these assertions do cost time and can thus be turned off.
  - \b \c EIGEN_MAX_ALIGN_BYTES - Must be a power of two, or 0. Defines an upper bound on the memory boundary in bytes on which dynamically and statically allocated data may be aligned by %Eigen. If not defined, a default value is automatically computed based on architecture, compiler, and OS.
  This option is typically used to enforce binary compatibility between code/libraries compiled with different SIMD options. For instance, one may compile AVX code and enforce ABI compatibility with existing SSE code by defining \c EIGEN_MAX_ALIGN_BYTES=16. In the other way round, since by default AVX implies 32 bytes alignment for best performance, one can compile SSE code to be ABI compatible with AVX code by defining \c EIGEN_MAX_ALIGN_BYTES=32.
  - \b \c EIGEN_MAX_STATIC_ALIGN_BYTES - Same as \c EIGEN_MAX_ALIGN_BYTES but for statically allocated data only. By default, if only  \c EIGEN_MAX_ALIGN_BYTES is defined, then \c EIGEN_MAX_STATIC_ALIGN_BYTES == \c EIGEN_MAX_ALIGN_BYTES, otherwise a default value is automatically computed based on architecture, compiler, and OS (can be smaller than the default value of EIGEN_MAX_ALIGN_BYTES on architectures that do not support stack alignment).
- Let us emphasize that \c EIGEN_MAX_*_ALIGN_BYTES define only a diserable upper bound. In practice data is aligned to largest power-of-two common divisor of \c EIGEN_MAX_STATIC_ALIGN_BYTES and the size of the data, such that memory is not wasted.
+ Let us emphasize that \c EIGEN_MAX_*_ALIGN_BYTES define only a desirable upper bound. In practice data is aligned to largest power-of-two common divisor of \c EIGEN_MAX_STATIC_ALIGN_BYTES and the size of the data, such that memory is not wasted.
  - \b \c EIGEN_DONT_PARALLELIZE - if defined, this disables multi-threading. This is only relevant if you enabled OpenMP.
    See \ref TopicMultiThreading for details.
  - \b \c EIGEN_DONT_VECTORIZE - disables explicit vectorization when defined. Not defined by default, unless 

doc/TopicLinearAlgebraDecompositions.dox

@@ -272,7 +272,7 @@ To get an overview of the true relative speed of the different decompositions, c
   <dt><b>Blocking</b></dt>
     <dd>Means the algorithm can work per block, whence guaranteeing a good scaling of the performance for large matrices.</dd>
   <dt><b>Implicit Multi Threading (MT)</b></dt>
-    <dd>Means the algorithm can take advantage of multicore processors via OpenMP. "Implicit" means the algortihm itself is not parallelized, but that it relies on parallelized matrix-matrix product routines.</dd>
+    <dd>Means the algorithm can take advantage of multicore processors via OpenMP. "Implicit" means the algorithm itself is not parallelized, but that it relies on parallelized matrix-matrix product routines.</dd>
   <dt><b>Explicit Multi Threading (MT)</b></dt>
     <dd>Means the algorithm is explicitly parallelized to take advantage of multicore processors via OpenMP.</dd>
   <dt><b>Meta-unroller</b></dt>

doc/TutorialSlicingIndexing.dox

@@ -112,7 +112,7 @@ Here are some examples for a 2D array/matrix \c A and a 1D array/vector \c v.
 </tr>
 </table>
 
-As seen in the last exemple, referencing the <i> last n </i> elements (or rows/columns) is a bit cumbersome to write.
+As seen in the last example, referencing the <i> last n </i> elements (or rows/columns) is a bit cumbersome to write.
 This becomes even more tricky and error prone with a non-default increment.
 Here comes \link Eigen::placeholders::lastN(SizeType) Eigen::placeholders::lastN(size) \endlink, and
 \link Eigen::placeholders::lastN(SizeType,IncrType) Eigen::placeholders::lastN(size,incr) \endlink:
@@ -222,7 +222,7 @@ i = ind[i];
 \endcode
 
 This means you can easily build your own fancy sequence generator and pass it to `operator()`.
-Here is an exemple enlarging a given matrix while padding the additional first rows and columns through repetition:
+Here is an example enlarging a given matrix while padding the additional first rows and columns through repetition:
 
 <table class="example">
 <tr><th>Example:</th><th>Output:</th></tr>

doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp

@@ -3,7 +3,7 @@ MatrixXd A = X + X.transpose();
 cout << "Here is a random symmetric matrix, A:" << endl << A << endl;
 X = MatrixXd::Random(5,5);
 MatrixXd B = X * X.transpose();
-cout << "and a random postive-definite matrix, B:" << endl << B << endl << endl;
+cout << "and a random positive-definite matrix, B:" << endl << B << endl << endl;
 
 GeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B);
 cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl;