Forms
Overview
A form of degree k is an alternating
tensor over a vector space V.
{% T(v_1, ... ,v_p, ... v_q,..., v_n) = - T(v_1, ... ,v_q, ... v_p,..., v_n) %}
The set of all alternating tensors of degree k is denoted {% \Lambda ^k %}.
Volume
One of the primary use of forms is in the calculation of n-dimensional volumes. In particular, given n vectors,
a n-form will assign a signed volume spanned by the vectors in accordance with the axioms
of the
Matrix Determinant
Topics
