Linear Operators

Linear operators are mathematical functions that transform one vector into another while preserving the operations of addition and scalar multiplication. In simpler terms, if you think of a vector as an arrow in space, a linear operator changes the direction or length of that arrow but does not change its essential straight-line nature. For example, if you double the length of the arrow or rotate it without bending, that's a linear operator at work. Linear operators are fundamental in various fields like physics and engineering, helping to model and solve complex problems involving linear relationships.