math / Linear Algebra / free
Vectors & Matrices
Move a vector through a transformation and track what survives.
Follow the mechanism1 / 3
A vector carries direction and magnitude. Its coordinates describe a directed quantity in a chosen basis.
linear transformationmatrix changes space
Focus the idea
matrix A[ 1.6 0.0 ; 0.0 0.8 ]
input v(2.0, 1.0)
output Av(3.2, 0.8)
area scale det A1.3
Transformation
The grid changes with the basis vectors: stretch changes how the whole space is organized.
A matrix transforms every vector in the same space. The determinant tells you how the transformation changes area; collapse has determinant zero and loses a dimension.