The equation T(u + v) = T(u) + T(v) represents a property of linear transformations in mathematics. Here, T is a function that takes a vector input, such as u and v , and produces another vector. This property states that when you apply the transformation T to the sum of two vectors, it is the same as applying T to each vector separately and then adding the results together. This property is essential in various fields, including linear algebra and functional analysis. It helps in understanding how linear systems behave and simplifies calculations involving transformations. When a transformation satisfies this property, it is classified as linear, which is a fundamental concept in mathematics and its applications.