Sentence examples for vector then the from inspiring English sources

Geometrically, If a and b are at right angles then a·b = 0, and if neither a nor b is a zero vector then the vanishing of the dot product shows the vectors to be perpendicular.

If shows the gradient vector, then the th element is found as (15).

If is the covariance matrix of the vector, then the variance of is (1.3).

If a matrix A is totally unimodular and b is an integral vector, then the polyhedron P = {x A x≤b} is integral.

If points' coordinates are in chronological feature vector, then the verification or even the identification leads to comparison. of the distance between two feature vectors.

Suppose that is an positive definite matrix and is an real vector, then the well-known Kantorovich inequality can be expressed as (1.1).

If we think of the parrot and the banana as vectors, then the punchline correctly states that the result is the length of the banana vector multiplied by the length of the parrot vector, multiplied by the sine of the angle between them.

In some batch processes, the variables' trajectories often show obviously functional nature and can be considered as smooth functions rather than just vectors, then the collected three-way data array essentially can be transformed into a two-way function matrix.

If we assume the input vectors of L subsequent transmissions to be Xn×L= [X1, X2,..., XL] and Y to be the matrix of the corresponding received vectors, then the decoder will be X ^ = argmax X ̃ f ¯ ( X ̃ | Y ), (15).

The precoder is designed in two phases: first the intercell interference is removed by applying a set of distributed precoding vectors; then the system is further optimized through power allocation.

Let θ be the permutation order of basis vectors, then the input matrix Hin, αof OLR-block is sorted as follows: θ ( i ) = arg min j ≠ θ ( k ) k < i h α, j. (17).