linear functionals

A linear functional is a mathematical concept used in areas like calculus and linear algebra. Think of it as a machine that takes an input (usually a vector) and provides a single output (a number) while following specific rules: it adds inputs and scales them. This means if you combine two inputs or multiply an input by a number, the output behaves accordingly. In essence, linear functionals help us understand and manipulate dimensions of space in a structured way, making them fundamental in various mathematical applications, including optimization and physics.