Dot product / centred dot (·) in LaTeX
The centred dot, \cdot, denotes multiplication in an inline expression, most commonly the scalar (dot) product of two vectors, but also plain multiplication where juxtaposition would be unclear.
LaTeX command
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\cdot is the standard symbol for the dot product, \mathbf{a} \cdot \mathbf{b}, which combines two vectors into a single scalar. This is a genuinely different operation from the cross product \times, which produces another vector, so the two symbols are not interchangeable.
For ordinary numeric or algebraic multiplication, \cdot is used whenever plain juxtaposition would be ambiguous or hard to read, for instance between two numbers () or between a coefficient and a bracket, while single-letter variables are usually just written next to each other, ab rather than .
\cdot is a single, small, centred dot, and should not be confused with \cdots, the larger ellipsis dots used to show a pattern continuing in a sum, product or sequence; they are different commands with different purposes.
Examples
$2 \cdot 3 = 6$multiplication between two numbers
$\mathbf{a} \cdot \mathbf{b}$the scalar (dot) product of two vectors
$\mathbf{a} \cdot \mathbf{b} = |\mathbf{a}||\mathbf{b}|\cos\theta$the dot product in terms of magnitudes and the angle between vectors
$f(x) = k \cdot x^2$a coefficient multiplied by a variable
Tips and common mistakes
- Use
\cdotfor the dot product and\timesfor the cross product, these are different vector operations, not two ways of writing the same thing. - Don't confuse
\cdot, a single multiplication dot, with\cdots, ellipsis dots showing a pattern continues, they are separate commands. - For products of single-letter variables, plain juxtaposition (xy) usually reads more cleanly than ; save
\cdotfor numbers or more complex terms. \cdotis not a decimal point, use a plain period for that.
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Convert your maths to LaTeX →FAQ
How do I type the dot product symbol in LaTeX?
Use \cdot inside maths mode, for example . No package is required.
What is the difference between \cdot and \times?
\cdot is used for the scalar dot product and general multiplication, while \times is used for the vector cross product, Cartesian products and scientific notation. For vectors they represent different operations entirely.
How do I write a centred multiplication dot?
Use \cdot, for example , which renders a small centred dot with correct spacing on both sides.
Is \cdot the same as a decimal point?
No, \cdot is a mid-height multiplication dot with operator spacing; a decimal point is a plain period at the baseline with no extra spacing.