Unleash the Power of 2D Transformations!
Compose and visualize 2D transformation matrices in an intuitive way. Perfect for students, educators, and anyone exploring linear transformations.
Input Transformation Matrices
Enter 2x2 matrices to compose. Click 'Add Matrix' to include more transformations in the sequence.
Composed Matrix
This is the resulting matrix after composing the input matrices. You can copy it for use elsewhere.
Understanding 2D Transformation Matrices
In linear algebra, a 2D transformation matrix is a 2x2 matrix that can be used to perform transformations in a 2-dimensional plane. These transformations include scaling, rotation, shearing, and reflection. By multiplying a point (represented as a column vector) by a transformation matrix, you can move, rotate, or scale that point.
Composing matrices involves multiplying multiple transformation matrices together to obtain a single matrix that represents the combined effect of all transformations applied in sequence. This tool allows you to easily compose a series of 2D transformations by inputting individual matrices and calculating their product. This is useful in computer graphics, robotics, and various engineering fields to efficiently apply complex transformations.
Learn more about transformation matrices on Wikipedia and explore linear algebra concepts on Khan Academy.