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Quaternions are a sort of extension of the idea of complex numbers. While complex numbers are in two dimensions, quaternions are in four dimensions - the three non-real axes are traditionally labeled i, j, k. The way multiplication is defined in quaternions, it is non-commutative.
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Professor
Beau
RossA quaternion is a mathematical concept in the field of algebra. It is an extension of the complex numbers and consists of four components: a real part and three imaginary parts. Quaternions are often used in computer graphics and robotics to represent three-dimensional rotations and orientations.
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How you represent rgb color by quaternion in matlab?
we can represente a RGB color in matlab by a pure quaternion q=0+R*I+G*J+B*K we apply the function q=quaternion(0,R,G,B); for this you must download the qtfm toolbox.
Can you add speed with velocity?
Yes, speed is a scalar and velocity is a vector, adding them together is called a quaternion or complex motion (s + v) = [s,v]. Complex numbers in geometry are 2 dimensional quaternion subsgroups.
What is a vector quatinty?
A vector is a part of a more general number or quantity, called a Matrix or Quaternion. Vectors were developed by William Rowan Hamilton as part of a Quaternion. The Quaternion consists of a scalar part 1 and three vectors I ,J and K.. The scalar is a real number and InJ and K are vector numbers, where I^2 = J^2 = K^2 = -1.. Vectors denote directions such as an axis in space, Ix + Jy + Kz. Quaternions Q = s + V = Q(cos(Q) + Vsin(Q)) = [cos(Q), sin(Q)(I + J + K)] . The Quaternion is vector if the angle is an even multiple 90 degrees and the Quaternion is a vector when the angle is a odd multiple of 90 degrees.. If the angle is not a multiple of 90 degrees, the Quaternion is part scalar and part vector. Most variables in physics are Quaternions. ============================================ A 'vector' quantity is a quantity that has both a size and a direction. Examples are: force, velocity, acceleration, and electric field. A 'scalar' quantity is a quantity that has size but no direction. Examples are: cost, temperature, speed, and volume.
Proof or Disprove 'If every proper subgroup of G is cyclic then G must be cyclic'?
No! Take the quaternion group Q_8.
What is the role of mathematics in the field of physics?
The Laws of Physics are mathematical and mathematics allows one to read and understand the Physical Laws.Before Newton, mathematics was seen as a tool for Physics. Now mathematics is the microscope and telescope for physics.The Universe consists of four dimensions (quaternions) and Quaternion Mathematics is rarely known among physicists and seldom taught.Consequently, much of the mysteries of "dark" physics is the result of lack of knowledge of Quaternion Mathematics.
