LINEAR FORM

LINEAR FORM - in an n-dimensional linear space - a functiondefined for all vectors of space , taking numerical values (in a certain field) and linear, i.e., having the properties:

,,

for any couple and any .

If are the coordinates of a vector in a given basis, then LINEAR FORM has the form: . Thus, each LINEAR FORM is a polynomial of the first degree of the coordinates of the vector.LINEAR FORM is the covariant tensor of the first valency. LINEAR FORM also called a linear functional on a finite-dimensional space .