Orthogonality | Chapter 3 Applied Linear Algebra

In the third video in this series on Applied Linear Algebra, we'll start by generalizing the concept of length to arbitrary vector spaces using inner products and norms. This introduces us to orthogonality -- when two vectors have an inner product equal to zero. We are then able to construct spaces and subspaces that are spanned by orthonormal bases, using the Gram-Schmidt algorithm. Matrices, also, can be orthogonal. Orthogonal matrices give rise to unitary transformations of objects and are used frequently in video games and other numerical applications

Music "Everything" by Vi Hart