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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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A 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.
What is boson and fermion?
Bosons and Fermions are parts of Quaternion Electronic Particles. The Boson is the Quaternion Scalar part and the Fermion is the Quaternion Vector part. Quaternions are four dimensional "particles" a Boson and a three dimensional FermionThe Quaternion Unit can be described by Q= Cos(Spin) + v Sin(Spin) where v is the unit vector. The Quaternion consists of a scalar part the Boson = Cos(Spin) and a vector part the Fermion = v Sin(Spin).When the angle Spin = n pi/2 if n is a multiple of 1 then the Quaternion Unit is a positive Fermion;If n is a multiple of 2 then the Quaternion is a negative Boson;if n is a multiple of 3 then the Quaternion is a negative Fermionif n is a multiple of 4, then the Quaternion is a Positive Boson.In general Bosons are even spin angles of pi/2 and Fermions are odd spin angles of pi/2.If the spin angel is not a multiple of pi/2 then the Quaternion is the sum of a Boson and a Fermion.This looks like Complex Numbers. because it is. Complex Numbers are a Quaternion 2 dimensional subgroup with Boson and a single vector Fermions.
What is the identity element of the quaternion group?
If you mean in the group {1, -1, i, -i, j, -j, k, -k}, the identity element is 1.
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.
What is the foundation of space science?
The foundation of space science is Quaternion Space and Quaternion Mathematics. A Quaternion Space , Q: Q= r + Ix + Jy + Kz = r + R = [r,R] a 4D space consisting of 1 real dimension r=ct (where c is the speed of light and t is time) and 3 vector dimensions R= Ix + Jy + Kz. Other Quaternion Quantities are: Energy W and Force and Momentum and motion are quaternion quantities. e.g. The law of gravity W = -mGm/r + mcV = [-mu/r, cmV] . A Quaternion Mathematics : A=[a,A] and B=[b,B] A+B = [a,A] + [b,B]= [a+b, A +B] AB= [a,A][b,B] = [ab - A.B, aB +Ab + AxB] A Quaternion Calculus; X= [d/dr, Del] XB= [d/dr,Del] [b,B] = [db/dr -Del.B, dB/dr + Del b + DelxB]
What are other words that mean 4?
'''quadrigeminal, quadripartition, quadrivium, quadrumvirate, quadruple, quadruplet,''' '''quadruplets, quartet, quartette, quaternary, quaternion, quaternity, tetrad,''' '''tetralogy, quad, quadrilateral'
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 the scientifical definition for force?
Force is the pressure of something against another object.
A scalar is a quantity that has?
A scalar quantity has an angle which is an even multiple of 90 degrees. A vector quantity has an angle which is an odd multiple of 90 degrees. A quaternion has any angle and includes the scalar and the vector; quaternion q = cos(angle) + unit-vector sin(angle)
What is the meaning of scalar?
In the quaternion analysis, a quantity that has magnitude, but not direction; -- distinguished from a vector, which has both magnitude and direction.
Transverse and longitudinal waves both?
Quaternion waves, e.g. earthquake wave, P and S waves..
What does the kinetic energy and potential energy equal together?
Quaternion Energy if the Kinetic Energy is a vector energy.
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.
