Linear Algebra
Explore the mathematics of vector spaces and linear mappings between them
Topics
Vectors
Vectors are mathematical objects that have both magnitude and direction. They are fundamental to linear algebra and are represented as arrays of numbers.
Vector Operations
Addition
v + w = (v₁+w₁, v₂+w₂, ..., vₙ+wₙ)
Scalar Multiplication
c·v = (c·v₁, c·v₂, ..., c·vₙ)
Dot Product
v·w = v₁w₁ + v₂w₂ + ... + vₙwₙ
Cross Product (3D)
v×w = (v₂w₃-v₃w₂, v₃w₁-v₁w₃, v₁w₂-v₂w₁)
Vector Properties
Magnitude
|v| = √(v₁² + v₂² + ... + vₙ²)
Direction
Unit vector: û = v/|v|
Interactive vector visualization will be added soon. This will show vector addition, scalar multiplication, and other operations in 2D and 3D space.