Linear Transformation Matrix Calculator
Find transformation matrices for rotations, reflections, scaling, and shearing
About this calculator
The Linear Transformation Matrix Calculator is a powerful tool that generates transformation matrices for common geometric operations including rotations, reflections, scaling, and shearing in 2D and 3D space. This calculator is essential for students, engineers, and mathematicians working with computer graphics, linear algebra, or geometric transformations. It eliminates manual calculations and provides instant, accurate matrices that can be directly applied to transform vectors and coordinate points in mathematical applications.
How to use
Select the type of transformation you need (rotation, reflection, scaling, or shearing) from the dropdown menu. Enter the required parameters such as angles for rotations, scale factors for scaling, or axis specifications for reflections. Click calculate to instantly generate the corresponding transformation matrix with step-by-step explanations.
Frequently asked questions
What is a linear transformation matrix?
A linear transformation matrix is a mathematical representation that describes how to transform vectors in space through operations like rotation, scaling, reflection, or shearing while preserving linear relationships.
Can this calculator handle 3D transformations?
Yes, the calculator supports both 2D and 3D linear transformations, generating appropriate 2x2, 3x3, or 4x4 matrices depending on the transformation type and dimensionality selected.
How do I apply the resulting matrix to vectors?
Multiply the transformation matrix by your vector coordinates using matrix multiplication. The result gives you the transformed vector coordinates in the new position or orientation.