#linear-algebra

Topics tagged "linear-algebra".

• Vector

  An arrow with magnitude and direction — the basic object that linear algebra adds, scales, and transforms.

• Matrix

  A rectangular grid of numbers that doubles as a recipe for transforming space.

• Linear Transformation

  A way of warping space that keeps grid lines straight, evenly spaced, and pinned to a fixed origin — exactly what a matrix encodes.

• Matrix Multiplication

  Multiplying matrices composes their transformations — do one, then the other — and the order matters.

• Linear Algebra

  The mathematics of vectors and the linear transformations that move them — the quiet engine beneath stability analysis, Fourier methods, and network ranking.

• Determinant

  A single number that says how much a transformation scales area or volume — and whether it flips orientation.

• Dot Product

  A single number, built from two vectors, that encodes the angle between them and how much one casts onto the other.

• Basis

  A set of reference directions that turns a vector into a list of numbers — change the directions and the numbers change, though the vector does not.

• PageRank

  A node's importance is the long-run chance a random surfer following links lands on it — the dominant eigenvector of the link matrix.

• Eigenvalues and Eigenvectors

  The special directions a transformation merely stretches — and the factors by which it stretches them — the hidden skeleton of a matrix.

• Singular Value Decomposition

  Every matrix factors into a rotation, a pure scaling, and another rotation — the most useful decomposition in applied linear algebra.