Visual Linear Algebra
No disconnected formulas. Start from one image: a matrix transforms a grid, and every topic grows from that.
From messy equations to the one picture connecting matrices, det, inverse, and Ax=b.
A narrative-first entry point: no formula dump, just the problem humans were trying to clean up.
Matrix columns show where the basis vectors land.
Start with the grid: a matrix is not just a table of numbers, it moves the whole plane.
Compose multiple transformations.
Once matrices are transforms, multiplication means doing one transform and then another.
Measure area scale, orientation, and collapse.
The determinant says how much area changes, whether orientation flips, and whether information collapses.
Undo a matrix transformation.
If the determinant is not zero, the transform did not collapse space and can be undone.
Find the input that lands on a target.
A system of equations asks which x gets transformed by A into the target vector b.
Later: Rank, null space, and eigenvectors become much clearer after determinants and inverses click.