What is quaternion theory?

Quaternions were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space, or, equivalently, as the quotient of two vectors.

What is quaternion used for?

Quaternions are vital for the control systems that guide aircraft and rockets. Let us think of an aircraft in flight. Changes in its orientation can be given by three rotations known as pitch, roll and yaw, represented by three arrays of numbers called matrices.

What is meant by quaternion?

1 : a set of four parts, things, or persons.

Who discovered quaternions?

William Rowan Hamilton
In the case of quaternions, however, we know that they were discovered by the Irish mathematician, William Rowan Hamilton on October 16*#, 1843 (we will see later how we come to be so precise). The early 19*# century was a very exciting time for Complex Analysis.

What kind of calculations can a quaternion be used for?

Quaternions find uses in both pure and applied mathematics, in particular for calculations involving three-dimensional rotations such as in three-dimensional computer graphics, computer vision, and crystallographic texture analysis.

When was the quaternion number system first described?

In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space.

When did William Rowan Hamilton describe the quaternions?

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 multiplication of two quaternions is noncommutative.

How is the rotation of a quaternion defined?

Any rotation of 3 – dimensional space about the origin can be defined by means of a quaternion P with norm 1. The rotation corresponding to P takes the vector X = x 1 i + x 2 j + x 3 k to the vector Y = y 1 i + y 2 j + y 3 k = P X P − 1 .