For 10 points, identify this binary operation which maps two elements of a vector space to an element of the underlying scalar field, as exemplified by the dot product in Euclidean spaces.
The Hermitian variety of this operation is a complex-valued bilinear form in which reversing the order of arguments of this operation is equivalent to taking a complex conjugate of this operation's result. A common example of this operation for the space of square-integrable real-valued functions is the integral of the product of two such functions from minus infinity to plus infinity. Hilbert spaces are vector spaces on which this operation is defined such that the norm results in a complete metric space. For 10 points, identify this binary operation which maps two elements of a vector space to an element of the underlying scalar field, as exemplified by the dot product in Euclidean spaces.
The Hermitian variety of this operation is a complex-valued bilinear form in which reversing the order of arguments of this operation is equivalent to taking a complex conjugate of this operation's result.
inner product