A linear transformation is a mathematical function that maps a vector space onto itself in a way that preserves the basic structure of the space, such as the distances and angles between vectors. It can be represented as a matrix multiplication or a combination of scaling, rotation, reflection, and shearing operations.
Some common examples of linear transformations include scaling, rotation, reflection, shearing, projection, and translation. These operations are commonly used in computer graphics, image processing, and engineering applications.
One example of a linear transformation in real life is the transformation of a 2D object, such as a map or a painting, into a 3D object, such as a globe or a sculpture. This transformation involves scaling, rotation, and translation operations that preserve the basic structure of the original object.
A linear transformation is a type of transformation that preserves the basic structure of a vector space, while a non-linear transformation does not. In other words, a linear transformation can be represented as a linear combination of basic operations, while a non-linear transformation cannot.
Linear transformations have many practical applications in fields such as computer science, engineering, physics, and economics. They are used to model and analyze real-world systems, perform image processing and computer graphics operations, and solve optimization problems.