Write mathematics. See it move.
Flow Math connects equations and graphs to moving 2D and 3D scenes. Explore matrices, vectors, and changing space in the Linear Algebra edition.
Open Linear AlgebraSee equations and spatial change as one flow
The Linear Algebra edition connects notebook matrices, vectors, and systems to real 2D and 3D scenes, with every change available to explore on a timeline.
Learn what to read from a visual scene
A scene is evidence, not decoration. Track where basis vectors land, how area and dimension change, and how solutions appear as intersections to connect symbolic work with the geometry it describes.
- A matrix chooses where the basis vectors land
- The first column of A is the destination of the standard basis vector e₁, and the second column is the destination of e₂. Every vector is a linear combination of those basis vectors, so their motion predicts how the entire grid and every vector will transform.
- The determinant is a signed scale factor
- In two dimensions, |det(A)| is the area scale; in three dimensions, it is the volume scale. A zero determinant means space collapses into a line or plane. A sign change shows that the orientation of the space has flipped as well as its size.
- Rank and null space show what remains and what disappears
- Rank is the dimension spanned by the outputs after a transformation. The null space contains every input direction that A sends to the zero vector. Seeing the surviving output beside the collapsed inputs explains information loss and the absence of an inverse.
- A system solution is a shared point on the graph
- The equation Ax=b asks for a point satisfying several conditions at once. In two dimensions it can appear as an intersection of lines; in three dimensions, as an intersection of planes. Row operations preserve the solution set while rewriting those conditions into a clearer form.
Before you start with Flow Math
What is Flow Math?
Flow Math is a mathematics visualization tool that connects equations and graphs to moving 2D and 3D scenes. The current Linear Algebra edition lets you play, refine, and share matrices, vectors, bases, and systems as visual stories.
How is it different from a linear algebra calculator?
A calculator usually emphasizes a final number or solution. Flow Math turns the order of declarations and operations into scenes, then lets you play, pause, and rewind the transformation process.
Which linear algebra topics can I visualize?
You can explore matrix transformations, vectors and bases, dot products, determinants, area and volume, lines, planes, systems, rank, null space, and row operations in one notebook flow.
Can I share a scene I create?
Yes. You can create a share link that carries the notebook and animation state so a student, teammate, or study group can open the same scene.
Do I need to install anything?
No separate program is required. Flow Math runs in a modern web browser, with a larger screen recommended when viewing the notebook and 3D scene together.