Copyedit documentation: typos, spelling
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				| @ -101,17 +101,16 @@ row and column position are to be stored. These variables should be of type | ||||
| \verbinclude Tutorial_ReductionsVisitorsBroadcasting_visitors.out | ||||
| </td></tr></table> | ||||
| 
 | ||||
| Note that both functions also return the value of the minimum or maximum coefficient if needed, | ||||
| as if it was a typical reduction operation. | ||||
| Both functions also return the value of the minimum or maximum coefficient. | ||||
| 
 | ||||
| \section TutorialReductionsVisitorsBroadcastingPartialReductions Partial reductions | ||||
| Partial reductions are reductions that can operate column- or row-wise on a Matrix or  | ||||
| Array, applying the reduction operation on each column or row and  | ||||
| returning a column or row-vector with the corresponding values. Partial reductions are applied  | ||||
| returning a column or row vector with the corresponding values. Partial reductions are applied  | ||||
| with \link DenseBase::colwise() colwise() \endlink or \link DenseBase::rowwise() rowwise() \endlink. | ||||
| 
 | ||||
| A simple example is obtaining the maximum of the elements  | ||||
| in each column in a given matrix, storing the result in a row-vector: | ||||
| in each column in a given matrix, storing the result in a row vector: | ||||
| 
 | ||||
| <table class="example"> | ||||
| <tr><th>Example:</th><th>Output:</th></tr> | ||||
| @ -133,8 +132,7 @@ The same operation can be performed row-wise: | ||||
| \verbinclude Tutorial_ReductionsVisitorsBroadcasting_rowwise.out | ||||
| </td></tr></table> | ||||
| 
 | ||||
| <b>Note that column-wise operations return a 'row-vector' while row-wise operations | ||||
| return a 'column-vector'</b> | ||||
| <b>Note that column-wise operations return a row vector, while row-wise operations return a column vector.</b> | ||||
| 
 | ||||
| \subsection TutorialReductionsVisitorsBroadcastingPartialReductionsCombined Combining partial reductions with other operations | ||||
| It is also possible to use the result of a partial reduction to do further processing. | ||||
| @ -176,7 +174,7 @@ The concept behind broadcasting is similar to partial reductions, with the diffe | ||||
| constructs an expression where a vector (column or row) is interpreted as a matrix by replicating it in  | ||||
| one direction. | ||||
| 
 | ||||
| A simple example is to add a certain column-vector to each column in a matrix.  | ||||
| A simple example is to add a certain column vector to each column in a matrix.  | ||||
| This can be accomplished with: | ||||
| 
 | ||||
| <table class="example"> | ||||
| @ -253,7 +251,7 @@ is a new matrix whose size is the same as matrix <tt>m</tt>: \f[ | ||||
| \f] | ||||
| 
 | ||||
|   - <tt>(m.colwise() - v).colwise().squaredNorm()</tt> is a partial reduction, computing the squared norm column-wise. The result of | ||||
| this operation is a row-vector where each coefficient is the squared Euclidean distance between each column in <tt>m</tt> and <tt>v</tt>: \f[ | ||||
| this operation is a row vector where each coefficient is the squared Euclidean distance between each column in <tt>m</tt> and <tt>v</tt>: \f[ | ||||
|   \mbox{(m.colwise() - v).colwise().squaredNorm()} = | ||||
|   \begin{bmatrix} | ||||
|      1 & 505 & 32 & 50 | ||||
|  | ||||
| @ -52,7 +52,7 @@ When doing so, a number of Eigen's algorithms are silently substituted with call | ||||
| These substitutions apply only for \b Dynamic \b or \b large enough objects with one of the following four standard scalar types: \c float, \c double, \c complex<float>, and \c complex<double>. | ||||
| Operations on other scalar types or mixing reals and complexes will continue to use the built-in algorithms. | ||||
| 
 | ||||
| In addition you can coarsely select choose which parts will be substituted by defining one or multiple of the following macros: | ||||
| In addition you can choose which parts will be substituted by defining one or multiple of the following macros: | ||||
| 
 | ||||
| <table class="manual"> | ||||
| <tr><td>\c EIGEN_USE_BLAS </td><td>Enables the use of external BLAS level 2 and 3 routines (currently works with Intel MKL only)</td></tr> | ||||
|  | ||||
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