- Abstract Algebra (3)
- Representation Theory (1)
- Ring Theory
- Algebra (51)
- Algebraic Geometry (2)
- Analytic Geometry (1)
- Applied Mathematics (202)
- Arithmetic (6)
- Calculus (112)
- Differential Calculus (69)
- Differential Equations (41)
- Integral Calculus (64)
- Limits (19)
- Multivariable Calculus (131)
- Precalculus (3)
- Tensor Calculus (1)
- Vector Calculus (1)
- Chaos Theory (1)
- Combinatorics (1)
- Polynomial Method (1)
- Complex Analysis (4)
- Complex Numbers
- Differential Geometry (3)
- Functional Analysis (2)
- Geometry (5)
- Fractals
- Non-Euclidean Geometry (2)
- Group Theory
- Lie Groups (2)
- History of Math (59)
- Linear Algebra (6)
- Mathematical Logic
- Set Theory (1)
- Mathematical Modeling
- Mathematics Education (11)
- Number Theory (1)
- Elliptic Curves (1)
- Quaternions
- Numerical Analysis (2)
- Partial Differential Equations (5)
- Probability (41)
- Queueing Theory
- Stochastic Process (2)
- Real Analysis (5)
- Recreational Mathematics
- Math Games
- Math Puzzles
- SAT Math (52)
- Statistics (49)
- Linear Models
- Stochastic Calculus
- Topology (5)
- K-theory (1)
- Point-Set Topology
- Trigonometry (18)

# Topics: Number Theory - Quaternions

### Quaternions

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. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two vectors.Graphical representation of quaternion units product as 90°-rotation in 4D-space, ij = k, ji = −k, ij = −ji