Duyệt các ví dụ hoạt ảnh Linear Algebra được tuyển chọn trong Math, bao gồm các cảnh Manim có thể tái sử dụng, chứng minh trực quan và ý tưởng sẵn sàng để giảng dạy.
Math · 3 hoạt ảnh
This animation introduces 2D vectors through visual demonstrations on a number plane. It shows a vector as an arrow, demonstrates scalar multiplication (stretching/shrinking), and vector addition using the tip-to-tail method. Component form and magnitude formula are displayed with MathTex.
Demonstrates the geometric meaning of eigenvalues and eigenvectors by applying a 2D linear transformation to the plane and contrasting how most vectors rotate and stretch while eigenvectors only stretch along their own span. The equation Av = λv is derived visually.
Visualizes how 2x2 matrices transform the plane by animating a NumberPlane grid through four key transformations: identity, 90-degree rotation, shear, and stretch. The basis vectors i-hat and j-hat are highlighted to show how the matrix columns determine the transformation outcome.
