A matrix is a transformation of the plane
This animation shows how the matrix A = [[2,1],[0,1]] transforms the plane by tracking where the basis vectors i-hat and j-hat land, forming the matrix's columns. The unit square stretches into a parallelogram, and its area grows by a factor of 2, matching the determinant exactly. Useful for students learning linear algebra, this visual connects abstract matrix entries to concrete geometric scaling and area transformation.
Narrated · 16:9 · every frame verified for overlaps, spacing and edges before rendering
The prompt that made it
The columns of the matrix A = [[2,1],[0,1]] are where the basis vectors i-hat and j-hat land. The unit square is carried to a parallelogram, and the determinant, 2, is exactly the factor by which area is scaled.
Make the next one in this series
- Show a matrix with a negative determinant flipping orientation of the plane
- Animate a shear transformation and explain why its determinant equals 1
- Compare two matrices with the same determinant but different shapes of transformation
