Condition numbers

A matrix condition number describes sensitivity of linear-system solutions to perturbations.

Different ways to understand it

No reviewed video yet. Explore the concept in a map or suggest a resource. Suggest a video

Matrix norms
Matrix norms quantify matrix size; induced norms measure maximum vector amplification.
Tensor products
Tensor products linearize bilinear maps and combine vector spaces.
Basis and dimension
A basis is a linearly independent spanning set; every vector has unique coordinates in that basis.
Determinants
The determinant of a square matrix tracks signed volume scaling and is nonzero exactly when the matrix is invertible.
Diagonalization
A matrix is diagonalizable when it has a basis of eigenvectors; having repeated eigenvalues does not by itself decide diagonalizability.