Orthonormal bases and the Gram-Schmidt process

Introduction to orthonormal bases

Coordinates with respect to orthonormal bases

Finding projection onto subspace with orthonormal basis example

Projections onto subspaces with orthonormal bases

Example using orthogonal change-of-basis matrix to find transformation matrix

The Gram-Schmidt process

Orthogonal matrices preserve angles and lengths

Gram-Schmidt example with 3 basis vectors

Gram-Schmidt process example