Linear Algebra Visualizer

Build real intuition for linear algebra. Enter points, apply a matrix, and watch the transformation unfold with every number color-coded to its basis vector.

Linear algebra clicks when you can see it.

Linear Algebra Visualizer turns the abstract machinery of 2D transformations into something you can watch, tweak, and reason about.

• Apply a 2×2 matrix and the app animates exactly where your shape lands
• Step by step explanation of the transformation for each point
• See the eigenvectors and values
• Plot your own points

WHY IT'S DIFFERENT

• Most tools show you the answer. This one shows you why the answer is the answer.
• The core insight: the columns of a matrix are where the basis vectors î and ĵ land — and this idea runs through every part of the interface.
• Column one is always red. Column two is always green.
• Those same colors thread through: * the transformed basis vectors on the canvas * the decomposition arrows * the step-by-step math
• The result: you can follow a single number from your matrix input all the way through to its effect on the output.

FEATURES:

• 2D coordinate canvas with static grid, warped grid, and axes
• See Eigenvectors and Eigenvalues in action
• Animated transformations that interpolate from identity to your target matrix
• Color-coded 2×2 matrix input with one-tap presets: Rotate 90°, Scale 2×, Shear, Reflect x-axis, Reflect y-axis
• Step-by-step math panel showing any selected point rewritten as x · col1 + y · col2, with every number color-matched to its column
• Decomposition overlay that draws the selected point as two arrows tip-to-tail — x · î' plus y · ĵ' — landing exactly where the transformed point sits

WHO IT'S FOR

• Students working through their first linear algebra course
• Graphics students
• Teachers who want a live demo on Mac
• Anyone who has stared at a matrix equation and thought "but why does it work?"

Download now to start taking your linear algebra to the next level!