Every space with this operation is a Banach space since this operation defines the norm or "length" of vectors, and these are generalized to integrals in Hilbert spaces, or vector spaces of functions.
Every space with this operation is a Banach space since this operation defines the norm or "length" of vectors, and these are generalized to integrals in Hilbert spaces, or vector spaces of functions. In a Euclidian vector space, this is the sum over two vectors of the products of their like components. For ten points, name the multiplication operation that, for two vectors a and b, is equal to the magnitude of a times the magnitude of b times the cosine of the angle between them.
Every space with this operation is a Banach space since this operation defines the norm or "length" of vectors, and these are generalized to integrals in Hilbert spaces, or vector spaces of functions.
{dot product} (or {scalar product} or {inner product}; accept {norm} before it’s mentioned)