Open learning resources by Flow Math
Go beyond memorizing definitions and calculations. Follow each mathematical claim to the evidence it leaves in a moving 2D or 3D scene. Every lesson includes the original runnable notebook and a direct animation link.
Connect row and column pictures of a system to elimination, LU, and inverse matrices.
5 lessonsThe column view mixes columns c1 and c2 of A to make target b
Read lessonSubtract twice the first row of A from the second to create a zero below the first pivot
Read lessonColumns c1 and c2 of A are the destinations of basis vectors i and j
Read lessonL remembers elimination multipliers while U is the upper-triangular result
Read lessonWhen A moves space, x moves from (1, 1) to (3, 2)
Read lessonGrow from linear combinations to independence, bases, the fundamental subspaces, and transformations.
7 lessonsA vector is an arrow with both magnitude and direction
Read lessonCompare u and v from the same origin
Read lessonA linear combination multiplies each vector by a coefficient and then adds them
Read lessonNeither a nor b is a scalar multiple of the other, so they provide two directions
Read lessonIndependent vectors such as b1 and b2 that generate every direction form a basis
Read lessonA removes the z direction from three-dimensional space
Read lessonDiagonal matrix S keeps the axis directions but doubles horizontal length
Read lessonCarry the right angle created by a dot product into projection and least-squares error.
3 lessonsThe dot product measures how much two vectors face the same direction
Read lessonA projection is the shadow of a vector on an axis or subspace
Read lessonWhen target b is not on direction a, choose its closest shadow p
Read lessonRead a determinant as an area or volume scale and watch a dimension disappear when it is zero.
2 lessonsStart with directions preserved by a transform and see how diagonalization simplifies the action.
2 lessonsRead positive definiteness as energy and split SVD into rotate, scale, rotate.
2 lessonsSee how conditioning magnifies input error and how repeated computation converges toward one direction.
2 lessonsUse constraint vertices and payoff matrices to explore optimization applications.
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Flow Math is a visual mathematics project by Made by need that helps people understand equations as moving scenes. The public Linear Algebra edition connects matrices, vectors, bases, determinants, rank, null space, and systems to runnable notebooks and 2D or 3D scenes. It is not an official course of a school or educational institution.
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Each lesson begins with one mathematical claim and the visual evidence needed to test it. It announces an operation, moves the real mathematical objects, and leaves the conclusion visible in the final scene. Playback, pause, rewind, and camera exploration let you inspect the result yourself.
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Email us about mathematical errors, scene problems, accessibility, or privacy requests. For a reproducible issue, include your environment and a shared URL when possible.
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