Sentence examples for case of a quaternion from inspiring English sources

in the case of a quaternion q.

For example, in the case of a quaternion algebra Q L (a), its realization (8) enables to compute its arithmetic operation efficiently.

Also the particular case of a general quaternion Wiener noise is studied and an extension of the Cameron-Martin formula is presented.

First, we study the detection of a quaternion deterministic signal in quaternion Gaussian noise.

The four-dimensional structure of a quaternion allows us to give a more general definition of a quaternion Wiener process in a similar way to [15].

This can be obtained from the single value decomposition of the covariance matrix (Kabsch, 1976) or from the solution of the eigenvalue equation of a quaternion derived matrix (Hung et al., 2011; Liu et al., 2010).

Firstly, we address the problem of detecting a quaternion deterministic signal in quaternion Gaussian noise and a version of Pitcher's Theorem is given.

Finally, the problem of detecting a quaternion random signal in quaternion white Gaussian noise is tackled.

In making a parchment or vellum codex, a large sheet was folded to form a folio of two leaves, a quaternion (quarto) of four, or even an octavo of eight.

In this paper, using the construction of Clifford algebras, we associate to the set of generalized Fibonacci quaternions a quaternion algebra A (i.e., a Clifford algebra of dimension four).

(19)The conjugate of a dual quaternion is defined based on the conjugate of quaternion as follows.