Gram–Schmidt process

Independent vectors are orthogonalized by subtracting projections onto earlier directions.

Different ways to understand it

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

Orthonormal bases
An orthonormal basis consists of mutually orthogonal unit vectors spanning the space.
QR factorization
A matrix factors into an orthonormal-column factor and an upper-triangular factor under suitable dimensions.
Basis and dimension
A basis is a linearly independent spanning set; every vector has unique coordinates in that basis.
Condition numbers
A matrix condition number describes sensitivity of linear-system solutions to perturbations.
Determinants
The determinant of a square matrix tracks signed volume scaling and is nonzero exactly when the matrix is invertible.