📖 About This Experiment
Explore the foundations of linear algebra: vectors as arrows in space, basis vectors that define coordinate systems, and linear transformations that stretch, rotate, and shear space. Visualize how matrices transform vectors.
💡 Key Concepts
- •Vectors: Quantities with magnitude and direction
- •Basis: Set of linearly independent vectors that span a space
- •Linear Transformation: Function preserving vector addition and scaling
- •Matrix: Rectangular array representing linear transformations
- •Dot Product: Measures similarity and projection
🔢 Key Formulas
Vector Magnitude
||v|| = √(x² + y² + z²)
Dot Product
v·w = ||v|| ||w|| cos(θ)
Matrix Transformation
Av = b