Conjugate "to care" - English conjugation

The conjugate of a quaternion is similar to the complex conjugate and transposition of Clifford algebra elements (also known as inversion). Let us quaternion to define it. The conjugate of q is a quaternion. This is represented by q *, q, qt or. A conjugate is a union that means it is its own inversion. Therefore, to return to the original element, we conjugate the element twice. The conjugate of the product of the two quaternions is the product of the conjugate in reverse order. In other words, if p and q are quaternions, not p * q * but (pq) * = q * p *.

In addition to the meaning given above, the term "conjugate" can also mean that element a is r ar - 1, where r is some nonzero quaternion . All elements conjugate to a given element (in the conjugate of this word) have the norm of the same real part and same vector part. (Thus, in another sense, conjugation is one of the conjugates in this sense.) Therefore, a multiplicative set of quaternions other than 0 passes through a copy of R 3 consisting of a quaternion with a nonzero real part To do. The conjugation goes well. The conjugate of the unit quaternion (the quaternion of absolute value 1) and the real part cos (θ) is the rotation angle 2θ, and the rotation axis is the direction of the vector part. Advantages of quaternions are as follows.

Where * denotes complex conjugate. The conjugate of the scalar potential is mapped to the body of the manifold and conversely the conjugate of the scalar potential is mapped to the body of the manifold. In mathematics, if f (z) is a regular function restricted to a real number, it has complex conjugate properties of f (z) = f * (z *), and when it is satisfied it becomes the above equation. The first successful classical unified field theory was developed by James Clerk Maxwell. In 1820, Hans Christian Ostern found out that the current exerted a force on the magnet, and in 1831 Michael Faraday observed that the time-varying magnetic field induced a current. Prior to that, electricity and magnetism were regarded as irrelevant phenomena. In 1864 Maxwell published a famous paper on the theory of electromagnetic field mechanics.