Blog Post··5 min read
Determinants and Invertibility
The determinant measures how much a matrix stretches or squishes space — and whether it flips orientation. When it's zero, information is lost and the matrix can't be inverted.
Tag: geometry
Blog Post··7 min read
Eigenvalues and Eigenvectors
Most vectors get rotated and scaled when multiplied by a matrix. Eigenvectors are the special directions that only get scaled — and their scaling factors, the eigenvalues, reveal everything about a matrix's long-term behavior.
Blog Post··9 min read
Inner Products and Cosine Similarity
What does it mean for two vectors to be similar? Inner products measure alignment between vectors — and cosine similarity is just the dot product with magnitudes divided out.
Blog Post··8 min read
Matrices as Linear Maps
A matrix is not just a grid of numbers — it's a function that transforms space. This post builds the geometric intuition for matrix-vector multiplication as rotation, scaling, and shearing.
Blog Post··8 min read
Vectors: Direction, Magnitude, and the Geometry of Space
Vectors are the atoms of linear algebra — everything else is built on them. This post builds intuition for what a vector is, how addition and scaling work geometrically, and why norms give us a way to measure the world.