It is relatively straightforward to see that the row vector g \ mathcal { Q } corresponds, in the same way, to the reduction of g ( x ) ^ q modulo f ( x ).
42.
When using [ binary number | binary ] representation of input [ row vector | vectors ], activation values will be 0 through 1, where 0 indicates no activation overlap and 1 indicates full activation overlap.
43.
These points of view are related by the canonical inner product on "'R " "'n ", which identifies the space of column vectors with the dual space of row vectors.
44.
Although defined in different terms ( column vectors versus row vectors, or forces versus motions ) static rigidity and first-order rigidity reduce to the same properties of the underlying matrix and therefore coincide with each other.
45.
The set of all row vectors forms a vector space called "'row space "', similarly the set of all column vectors forms a vector space called "'column space " '.
46.
And in this formulation, the four-vector is represented as a Hermitian matrix ( the matrix transpose and complex conjugate of the matrix leaves it unchanged ), rather than a real-valued column or row vector.
47.
The matrix product of a column and a row vector gives the dyadic product of two vectors "'a "'and "'b "', an example of the more general tensor product.
48.
A row vector representation is also legitimate, although in the context of general curvilinear coordinate systems the row and column vector representations are used separately for specific reasons see Einstein notation and covariance and contravariance of vectors for why.
49.
The elements of A are the pairwise inner products of the row vectors of B . Let U be a unitary matrix that diagonalizes A ( i . e ., U ^ {-1 } AU is diagonal ).
50.
The singularities are avoided when considering and manipulating the rotation matrix as orthonormal row vectors ( in 3D applications often named'right'- vector,'up'- vector and'out'- vector ) instead of as angles.
