Linear Transformation Calculator
Apply linear transformations to vectors and visualize rotations, scaling, and reflections
About this calculator
The Linear Transformation Calculator applies mathematical transformations to vectors and provides visual representations of geometric operations. This powerful tool helps students, engineers, and researchers understand how matrices transform vectors through rotations, scaling, reflections, and shearing. By combining numerical calculations with interactive visualizations, users can instantly see how linear transformations affect vector positions and orientations in 2D or 3D space, making complex mathematical concepts more intuitive and accessible.
How to use
Enter your transformation matrix and input vector into the designated fields. Select the type of transformation you want to apply (rotation, scaling, reflection, or custom matrix). Click calculate to see the transformed vector coordinates and view the interactive visualization showing both original and transformed vectors with grid references.
Frequently asked questions
What types of linear transformations can this calculator perform?
The calculator handles rotations, scaling, reflections, shearing, and custom matrix transformations in both 2D and 3D coordinate systems.
Can I visualize multiple transformations at once?
Yes, you can apply sequential transformations and see the cumulative effect on your vectors with step-by-step visual progression.
Does the calculator work with non-square matrices?
The calculator primarily works with square transformation matrices, but supports rectangular matrices for dimension-changing transformations between different vector spaces.