Dot operator

Usually multiplication between two expressions. In a ⋅ b, the dot separates the two factors. Between vectors it signals a dot product, also called a scalar product, whose result is a plain number rather than another vector. In abstract algebra, it can name the operation being studied, where writing ab would leave that operation invisible.

No single person invented it. Dots appear in earlier mathematical writing, but historians dispute whether some early examples meant multiplication or merely separated numbers. A 1694 letter from Johann Bernoulli uses a multiplication dot, and Leibniz explicitly promoted the dot in 1698 because × could be confused with the letter x.

Is ⋅ the same as ·?

No; they are separate characters that look almost identical. ⋅ is the mathematical dot operator. · is the middle dot, a punctuation mark whose height and spacing vary more between fonts. Use ⋅ when the text should carry mathematical meaning; use · when you mean punctuation.

The surrounding notation settles the reading better than the dot itself. Between vectors it means dot product; between units such as kg and m it joins multiplied units; in everyday writing, style guides may prefer × because readers recognise it faster.