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, in mathematics, are a non-commutative extension of complex numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. They find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations, such as in 3D computer graphics. Since the affine transformations representable by matrices are a superset of quaternion rotations, matrices are employed as a computationally suboptimal but geometrically equivalent orientation representation in many calculations. Vectors cannot represent rotations per se, only directions, and so are generally unsuitable unless the calculation in question assumes a fixed "up" direction.
In modern language, quaternions form a 4-dimensional normed division algebra over the real numbers. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by (Unicode ℍ). It can also be given by the Clifford algebra classifications Cℓ0,2(R) = Cℓ03,0(R). The algebra H holds a special place in analysis since, according to the Frobenius theorem, it is one of only three finite-dimensional division rings containing the real numbers as a subring.Graphical representation of quaternion units product as 90°-rotation in 4D-space, ij = k, ji = −k, ij = −ji
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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.
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]
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.
Science words that starte with a q?
quartz (a type of rock) quasar quark quaternion (this is technically a mathematical term)
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.
