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25 In Eigen, a reduction is a function taking a matrix or array, and returning a single
27 returning the sum of all the coefficients inside a given matrix or array.
38 The \em trace of a matrix, as returned by the function \c trace(), is the sum of the diagonal coefficients and can equivalently be computed <tt>a.diagonal().sum()</tt>.
47 These operations can also operate on matrices; in that case, a n-by-p matrix is seen as a vector of size (n*p), so for example the \link MatrixBase::norm() norm() \endlink method returns the "Frobenius" or "Hilbert-Schmidt" norm. We refrain from speaking of the \f$\ell^2\f$ norm of a matrix because that can mean different things.
65 - \link DenseBase::all() all() \endlink returns \b true if all of the coefficients in a given Matrix or Array evaluate to \b true .
66 - \link DenseBase::any() any() \endlink returns \b true if at least one of the coefficients in a given Matrix or Array evaluates to \b true .
67 - \link DenseBase::count() count() \endlink returns the number of coefficients in a given Matrix or Array that evaluate to \b true.
88 a Matrix or Array. The simplest examples are
91 the location of the greatest or smallest coefficient in a Matrix or
111 Partial reductions are reductions that can operate column- or row-wise on a Matrix or
117 in each column in a given matrix, storing the result in a row-vector:
145 within a matrix. With column-wise partial reductions this can be coded as:
157 though the \link DenseBase::colwise() colwise() \endlink visitor, obtaining a new matrix whose
179 constructs an expression where a vector (column or row) is interpreted as a matrix by replicating it in
182 A simple example is to add a certain column-vector to each column in a matrix.
195 to every column of the matrix. Alternatively, it can be interpreted as repeating the vector \c v four times to
196 form a four-by-two matrix which is then added to \c mat:
205 is not clear what they would do. If you want multiply column 0 of a matrix \c mat with \c v(0), column 1 with
209 and cannot be a Matrix. If this is not met then you will get compile-time error. This also means that
210 broadcasting operations can only be applied with an object of type Vector, when operating with Matrix.
226 Broadcasting can also be combined with other operations, such as Matrix or Array operations,
230 the nearest neighbour of a vector <tt>v</tt> within the columns of matrix <tt>m</tt>. The Euclidean distance will be used in this example,
250 is a new matrix whose size is the same as matrix <tt>m</tt>: \f[