Transformation Matrix Applicator

Visualize and apply transformation matrices to points and vectors. Enter your matrix and points to see the transformation in action.

Transformation Matrix:

Enter your transformation matrix in JSON array format. For example: [[1, 0], [0, 1]] for a 2D identity matrix.

Points / Vectors:

Enter points or vectors to transform, as a JSON array of arrays. For example: [[1, 2], [3, 4]].

Transformed Points / Vectors:

Visualization

Understanding Transformation Matrices

A transformation matrix is a powerful tool in linear algebra used to perform various geometric transformations such as translation, rotation, scaling, and reflection on vectors and points. By multiplying a matrix with coordinate vectors, we can efficiently transform these coordinates in space.

How to Use This Tool:

Enter Matrix: Input your transformation matrix as a JSON array. For 2D transformations, use a 2x2 matrix, e.g., [[a, b], [c, d]].
Enter Points: Provide the points or vectors you wish to transform, also in JSON array format. For 2D points, use [[x1, y1], [x2, y2]].
Click 'Transform': Execute the transformation. The transformed points will be displayed below, and visualized on the graph.
'Reset' Button: Clears all inputs and outputs to start fresh.
'Copy Output': Copies the transformed points in JSON format to your clipboard.

This tool is designed to help students, educators, and professionals quickly apply and visualize linear transformations, making it easier to understand the effects of matrices in a geometric context.