Description
A detailed tutorial on orthogonal complements. Step by step tutorial including several examples of orthogonal complements for reference.
Overview
The orthogonal complement of a subspace of an inner product space is the set of all vectors in the inner product space that are orthogonal to every vector in the subspace. This can be expressed mathematically in the formula 
Description
A detailed tutorial on linear subspaces and how to identify linear subspaces. Step by step tutorial including several examples of linear subspaces for reference.
Overview
A linear subspace is usually referred to as simply a subspace, when it needs to be distinguished from other types of subspaces. Linear subspaces are also sometimes referred to as vector subspaces. In mathematical terms, to identify a linear subspace, we say that K is a field (or a set, like of real numbers), and V is a vector space over K. Elements of V are vectors and elements of K are scalars. W is said to be a subset of V. If W is a vector space itself, with the same vector space operations as V, then it has a subspace of V.
