The first fundamental form of a surface is essentially an instance of it performed on two elementsof the tangent space. The Bogoliubov type of this operation takes operators as arguments, and in aMinkowski space this operation is non-degenerate rather than positive definite. Over a complexHilbert space, this object is necessarily a Hermitian form, and a Hilbert space is a complete abstractvector space for which this (*) operation is defined. If the result of this operation on two elements iszero, they are orthogonal, and setting both arguments of this operation equal gives the norm. A specificcase of this operation is
The first fundamental form of a surface is essentially an instance of it performed on two elementsof the tangent space. The Bogoliubov type of this operation takes operators as arguments, and in aMinkowski space this operation is non-degenerate rather than positive definite. Over a complexHilbert space, this object is necessarily a Hermitian form, and a Hilbert space is a complete abstractvector space for which this (*) operation is defined. If the result of this operation on two elements iszero, they are orthogonal, and setting both arguments of this operation equal gives the norm. A specificcase of this operation is equal to a b cosine theta. For ten points, name this operation which maps twoelements of a vector space to a scalar, an example of which is the dot product in Euclidean space.
The first fundamental form of a surface is essentially an instance of it performed on two elementsof the tangent space.
Inner product [accept norm until mention; prompt on "dot product" until mention]