Multiplication table
A multiplication table is used to define a 'multiplication' operation for an algebraic system. Multiplication tables as they are used to teach schoolchildren multiplication are a grid where rows and columns are headed by the numbers to multiply, and the entry in each cell is the product of the column and row headings:
| 9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
× |
|
2×2 = 4 |
2 |
|
3×3 = 9 |
3×2 = 6 |
3 |
|
4×4 = 16 |
4×3 = 12 |
4×2 = 8 |
4 |
|
5×5 = 25 |
5×4 = 20 |
5×3 = 15 |
5×2 = 10 |
5 |
|
6×6 = 36 |
6×5 = 30 |
6×4 = 24 |
6×3 = 18 |
6×2 = 12 |
6 |
|
7×7 = 49 |
7×6 = 42 |
7×5 = 35 |
7×4 = 28 |
7×3 = 21 |
7×2 = 14 |
7 |
|
8×8 = 64 |
8×7 = 56 |
8×6 = 48 |
8×5 = 40 |
8×4 = 32 |
8×3 = 24 |
8×2 = 16 |
8 |
| 9×9 = 81 |
9×8 = 72 |
9×7 = 63 |
9×6 = 54 |
9×5 = 45 |
9×4 = 36 |
9×3 = 27 |
9×2 = 18 |
9 |
This table does not give the ones and zeros. That is because:
- Anything times zero is zero.
- Anything times one is itself. For example, 5×1=5.
Adding a number to itself is the same as multiplying it by two. For example, 7+7=14, which is the same as 7×2.
Multiplication tables can define 'multiplication' operations for groups, fields, rings, and other algebraic systems.
The following table is an example of a multiplication table for the unit octonions (see octonion, from which this example is taken).
| ·
| 1
| e1
| e2
| e3
| e4
| e5
| e6
| e7
|
| 1
| 1
| e1
| e2
| e3
| e4
| e5
| e6
| e7
|
| e1
| e1
| -1
| e4
| e7
| -e2
| e6
| -e5
| -e3
|
| e2
| e2
| -e4
| -1
| e5
| e1
| -e3
| e7
| -e6
|
| e3
| e3
| -e7
| -e5
| -1
| e6
| e2
| -e4
| e1
|
| e4
| e4
| e2
| -e1
| -e6
| -1
| e7
| e3
| -e5
|
| e5
| e5
| -e6
| e3
| -e2
| -e7
| -1
| e1
| e4
|
| e6
| e6
| e5
| -e7
| e4
| -e3
| -e1
| -1
| e2
|
| e7
| e7
| e3
| e6
| -e1
| e5
| -e4
| -e2
| -1
|
Referenced By
List of abstract algebra topics | List of group theory topics | List of mathematical topics (M-O) | Table (information)
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