## Quaternion

In mathematics, the **quaternions** are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. A feature of quaternions is that the product of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two vectors. Quaternions can also be represented as the sum of a scalar and a vector.

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### Some articles on quaternion:

**Quaternion**- Quotes

... I regard it as an inelegance, or imperfection, in

**quaternions**, or rather in the state to which it has been hitherto unfolded, whenever it becomes or seems to become necessary to ... The mathematical

**quaternion**partakes of both these elements in technical language it may be said to be "time plus space", or "space plus time" and in this sense it has, or at least involves a reference to ...

**Quaternions**came from Hamilton after his really good work had been done and, though beautifully ingenious, have been an unmixed evil to those who have touched them in any way ...

Versor

... In modern algebra, a versor or unit

... In modern algebra, a versor or unit

**quaternion**is a**quaternion**of norm one ... When used to represent a rotation, a versor will rotate any**quaternion**vector v through the angle θ around the unit vector r through the sandwiching product qvq−1 ... introduced by William Rowan Hamilton, in the context of his**quaternion**theory ...Classical Hamiltonian

... A right

**Quaternion**s - Classical Elements of A**Quaternion**-**Quaternion**- Right**Quaternion**... A right

**quaternion**is a**quaternion**whose scalar component is zero, The angle of a right**quaternion**is 90 degrees ... A right**quaternion**can also be thought of as a vector plus a zero scalar ... Right**quaternions**may be put in what was called the standard trinomial form ...Classical Hamiltonian

... Symbolically A

**Quaternion**s - Other Operators in Detail - Tensor... Symbolically A

**quaternion**is by definition the quotient of two vectors and the tensor of a**quaternion**is by definition the quotient of the tensors of these two vectors ... a useful formula for the tensor of a**quaternion**is It can also be proven from this definition that another formula to obtain the tensor of a**quaternion**is from ... The square root of the common norm of a**quaternion**is equal to its tensor A useful identity is that the square of the tensor of a**quaternion**is equal to the tensor of ...Classical Hamiltonian

... Taking the angle of a non-scalar

**Quaternion**s - Other Operators in Detail - Axis and Angle... Taking the angle of a non-scalar

**quaternion**, resulted in a value greater than zero and less than π ... When a non-scalar**quaternion**is viewed as the quotient of two vectors, then the axis of the**quaternion**is a unit vector perpendicular to the plane of the two vectors in this original ...