Algosim documentation: InnerProduct


Dot (inner, scalar) product of vectors.



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).


u ≔ ❨1, 0, 1, 1❩/√3; a ≔ ❨1, 5, 2, 1❩;
InnerProduct(a, u)
2.30940107676	(=(4/3)⋅√3)


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

The | operator is implemented by the InnerProduct function.

See also