Visualizations
Many visualizations and simulations were created with assistance from Google Gemini 3 Pro.
| Title | Description |
|---|---|
| Cofactor Expansion for 3×3 Determinants | A Step-by-Step Guide to Computing 3×3 Determinants |
| Cofactor Expansion for 4×4 Determinants | A Step-by-Step Guide to Computing 4×4 Determinants |
| Discrete-time Finite Markov Chains | Real-time simulation of state transitions and long-run behavior |
| Eigenvectors & Eigenvalues | Finding the invariant directions of a linear transformation |
| Electric Circuit Mesh Analysis | Analyzing electric circuits with LU/LUP decomposition |
| Fourier Transformation for Image Processing | Filtering images with Fourier frequencies |
| Geometric Proof of 2x2 Determinant | Flattening a Parallelogram to Compute Its Area |
| Gram–Schmidt in 2D | Step-by-step Orthogonalization for two vectors in 2D |
| Gram–Schmidt in 3D | Step-by-step Orthogonalization for three vectors in 3D |
| Handwritten Digit Classification using SVD | Classifying 28x28 images by projecting them onto orthogonal bases |
| Linear Transformations in 2D | An interactive study of planar linear transformations (featuring Aubie) |
| Linear Transformations in 3D | Exploring geometric interpretations of linear transformations in 3D |
| Matrix Diagonalization | Deconstructing a transformation: A = P D P⁻¹ |
| Orientation and Sign of Determinant | Orientation, Signed Area, and the Right-Hand Rule |
| Singular Value Decomposition (SVD) in 2D | Deconstructing a transformation: A = U Σ Vᵀ |
| Singular Value Decomposition (SVD) in 3D | Deconstructing a 3D transformation: A = U Σ Vᵀ |
| Subspaces in 3D Euclidean Space | Visualizing the Span of Vectors in 3D Euclidean Space |
| Vector Operations in 2D | Interactive playground for fundamental planar vector arithmetic |
| Vector Operations in 3D | Navigating vector space and cross products in 3D |
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