  In this paper we construct a linear space that parameterizes all invariant
bilinear forms on a given vertex algebra with values in a arbitrary vector
space. Also we prove that every invariant bilinear form on a vertex algebra is
symmetric. This is a generalization of the result of H. Li [J. Pure and Appl.
Algebra, 96(3):279-297, 1994], who proved this for the case when the vertex
algebra is non-negatively graded and has finite dimensional homogeneous
components.
  As an application, we introduce a notion of a radical of a vertex algebra. We
prove that a radical-free vertex algebra A is non-negatively graded, and its
component A_0 of degree 0 is a commutative associative algebra, so that all
structural maps and operations on A are A_0-linear. We also show that in this
case A is simple if and only if A_0 is a field.
