InnerProduct

Dot (inner, scalar) product of vectors.

Syntax

• InnerProduct(u, v)

  • u and v are vectors of the same dimension

Description

If u and v are vectors of the same dimension, then InnerProduct(u, v) is their dot (inner, scalar) product. If both vectors are real, so is InnerProduct(u, v). If one or both of the vectors are complex, the complex inner product is used and the result is a complex number (typewise, that is: its imaginary part may well be zero).

Examples

u ≔ ❨1, 0, 1, 1❩/√3; a ≔ ❨1, 5, 2, 1❩;

InnerProduct(a, u)

2.30940107676	(=(4/3)⋅√3)

Notes

The dot (inner, scalar) product between u and v can also be written u⋅v or (u|v).

The | operator is implemented by the InnerProduct function.

See also

• |

• ⋅

• × (cross, CrossProduct)