Sentence examples for matrix describing a from inspiring English sources

The transverse beam envelope analyses, such as error sensitivity, chromatic aberration, and emittance growth, are presented by applying second-order perturbation treatment to a formulated matrix describing a quasi-periodic lattice in the linear accelerator system.

This visualization represents the fact that quantum gates are unitary operators, i.e., they preserve the norm of the quantum state (if \(U\) is a matrix describing a single qubit gate, then \(U^{\dagger}U=I\), where \(U^{\dagger}\) is the adjoint of \(U\), obtained by transposing and then complex-conjugating \(U \).

Consider the case of a compound rotation matrix R representing successive rotations about three normalized axes, û, and such that (A.8 where a general, elemental rotation matrix describing a positive rotation of angleΨabout the axisêis given by (Wertz and Larson, 1999) (A.9 Using the properties of the cross-product matrix, the following additional property of interest may be derived (A.10).

This equation uniquely defines the symmetric, traceless 2 × 2 tensor Q m, where the exponential of a tensor is defined by the Taylor series of the exponential function, and Rot(Θ m ) denotes the matrix describing a counter-clockwise rotation by the angle Θ m.

The X matrix describes a distribution of the operators on the stages.

The extrinsic matrix describes a camera's "pose" including camera's rotation, pan-and-tilt, and location c in the world coordinate.

As shown in Table 1, the matrix describes a two-step learning trajectory from 'beginning designer' (that depicts assumptions about prior knowledge and skills of learners as they enter a learning progression) to 'informed designer' (that depicts what learners are expected to know and do by the end of the progression).

In simple words, this adjacency matrix describes a network in which two nodes i and j are linked if they are strongly correlated - the correlation between them is above a threshold level.

In addition to the already discussed oblique monolayer structure M1, also a rectangular unit cell is found, which in the real space can be expressed by the following commensurable epitaxial matrix (see Figure 4b): This matrix describes a commensurable, rectangular p 6 × 2) unit cell with the lattice parameters a = 1.53 nm and b = 0.72 nm.

Actually, there are two kinds of matrices, viz. a refraction matrix describing the refraction at a lens surface, and a translation matrix, describing the translation of the plane of reference to the next refracting surface, where another refraction matrix applies.

A similar transformation to Eq. (1) can be written: Δ m k = ∑ j A k, j ⋅ Δ μ a, j, (3)where A k,j is the sensitivity matrix describing transformation between a change in the k th moment and the change in absorption coefficient occurring in the j th layer.