Octonion Algebra Multiplication Tables

​
μ
1
μ
2
μ
3
symbolic coefficients
highlight negative coefficients
u
1
u
2
u
3
u
4
u
5
u
6
u
7
u
8
u
2
3
u
1
-
u
4
-3
u
3
-
u
6
-3
u
5
u
8
3
u
7
u
3
u
4
3
u
1
3
u
2
-
u
7
-
u
8
-3
u
5
-3
u
6
u
4
3
u
3
-3
u
2
-9
u
1
-
u
8
-3
u
7
3
u
6
9
u
5
u
5
u
6
u
7
u
8
5
u
1
5
u
2
5
u
3
5
u
4
u
6
3
u
5
u
8
3
u
7
-5
u
2
-15
u
1
-5
u
4
-15
u
3
u
7
-
u
8
3
u
5
-3
u
6
-5
u
3
5
u
4
-15
u
1
15
u
2
u
8
-3
u
7
3
u
6
-9
u
5
-5
u
4
15
u
3
-15
u
2
45
u
1
Multiplication tables for Cayley's octonion numbers incorporate three scalar coefficients. Modify these coefficients to change the resulting positions of negative coefficients.

External Links

Cayley Algebra (Wolfram MathWorld)

Permanent Citation

Michael Schreiber
​
​"Octonion Algebra Multiplication Tables"​
​http://demonstrations.wolfram.com/OctonionAlgebraMultiplicationTables/​
​Wolfram Demonstrations Project​
​Published: September 28, 2007