with edges defined by three of these objects has a volume of those three objects' box product.
A normed space named after these objects defines the notion of these objects' size. One type of these objects is left-multiplied by "A minus lambda I" to yield these objects' additive identity. According to Helmholtz's theorem, a mathematical construct composed of these objects can be uniquely specified by regional divergence, curl, and a boundary (*)  normal component. The basic definition of the CauchyÂ–Schwarz inequality in an inner product space is defined on these objects. A parallelepiped (para-LEL-uh-PIPE-id)  with edges defined by three of these objects has a volume of those three objects' box product. Two linearly dependent instances of these objects have a cross product of zero. For 10 points, name these mathematical objects that have both magnitude and direction, unlike scalars.
A normed space named after these objects defines the notion of these objects' size.
vector s [accept  vector  fields; accept eigen vector s until "Helmholtz's" is read]