2D Vector Transformation Calculator

Visualize how vectors are transformed by matrices. Enter a 2D vector and a 2x2 transformation matrix to see the result graphically and numerically.

Input Vector and Matrix

Vector (x, y):

Transformation Matrix (2x2):

Result

Transformed Vector:

Vector Visualization

Understanding 2D Vector Transformation

In linear algebra, a 2D vector transformation involves changing a vector in a two-dimensional space. This is often achieved using a 2x2 matrix, known as a transformation matrix. When you multiply a 2D vector by a transformation matrix, you get a new, transformed vector.

This tool helps visualize common transformations like scaling, rotation, and shear. By changing the values in the 2x2 matrix, you can observe how the original (blue) vector is transformed into the new (red) vector. This is fundamental in computer graphics, physics simulations, and many engineering fields.

For example, try using the matrix [[0, -1], [1, 0]] to see a 90-degree rotation, or [[2, 0], [0, 2]] for scaling by a factor of 2. Experiment to explore different transformations!