Orthogonal Complement

In this video we introduce a subspace orthogonal to another subspace which is called "orthogonal complement". If we have a subspace in a vector space, the orthogonal complement is the set of all the vectors that are orthogonal to the vectors that span first subspace. In other words, the inner product of the vectors in orthogonal complement with the vectors in the first subspace is zero. We use a 3D and also a 5D vector space to show what it actually is. In addition, we use the Gram-Schmidt Process in the 5D example to create an orthonormal basis set out of the linearly independet vectors we have for the two subspaces I earlier talked about.