Sentence examples for matrix multiplication the from inspiring English sources

We show that for several fundamental problems, including standard matrix multiplication, the Fast Fourier Transform, and comparison sorting, there exist optimal portable algorithms in that sense, for all combinations of machine parameters.

For example, in matrix multiplication, the carry chain of calculating the product of two numbers is broken by sending the partial sums and carries of the product to the accumulating operation instead of the whole finished word.

For the LDPCA encoder, approximately the same number of syndrome bits should be produced, and if it is implemented as an ordinary matrix multiplication, the number of operations becomes the same.

end{aligned} (121) Hence, by definition of matrix multiplication, the time domain total control matrix takes the form mathbf{R}(t) = sum_{l=1}^{n}G^{ l)}(t) mathbf {R}^{P_{l}} t-t_{l-1} boldsymbol{Lambda} t-t_{l-1} boldsymbol{

The OrthoMCL uses matrix multiplication, the operation with the minimal complexity n ω, where the exponent ω is a parameter.

Because of the non-commutative property of matrix multiplication, the equation can not be solved in closed form.

After a large number of rounds of mutation (matrix multiplications), the resulting vector of amino acid counts is invariant under mutation.

Therefore, once the commutator reaches the top, the matrix multiplication between the input buffer and the filter coefficient matrix is complete.

The size of the matrix and thus the computing cost of the matrix multiplication in the Equations (11) and (12) depend on the number of landmarks in the state vector.

Any m-by-n matrix A gives rise to a linear map from Fn to Fm, by the following :\mathbf x = (x_1, x_2, \cdots, x_n) \mapsto \left(\sum_{j=1}^n a_{1j}x_j, \sum_{j=1}^n a_{2j}x_j, \cdots, \sum_{j=1}^n a_{mj}x_j \right), where \sum denotes summation, or, using the matrix multiplication of the matrix with the coordinate vector : :.

The following properties can be easily deduced from the definition of matrix multiplication and the associativity of the ⊕ operation (in each property the participating matrices are assumed to be of the appropriate sizes).