A quadratic form on a vector space V over a field F is a function Q : V to F such that
A vector v≠0 is isotropic if β(v, v) = 0; it is defined to be singular if Q(v) = 0.
The radical of V is the subspace of vectors u such that β(u, v) = 0 for all v∈V.
The quadratic space defined by the quadratic form represented by a square matrix Q over a field.
The value Q(v), where Q is the quadratic form attached to the ambient space of the vector v.
Determine whether the quadratic space V contains a singular vector; if it does, assign a representative as the second return value.
If u is a singular vector in a quadratic space V this function returns a singular vector v such that β(u, v) = 1, where βis the polar form of the space, provided u is not in the radical of V.[Next][Prev] [Right] [Left] [Up] [Index] [Root]