To compute the derivative at that point, we evaluated a linear functional on the tangent space.

The simplest example of a linear function is f(x) = 2x + 3, whose graph is a straight line.

In functional analysis, linear functionals play a central role in defining dual spaces.

In algebra class, we graphed several linear functions to compare their slopes and intercepts.

The positive linear functional defined on C([0,1]) assigns a non-negative value to every non-negative continuous function.

In the seminar, she explained how positive linear functionals determine the state space of a C*-algebra.