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.
Description
A detailed tutorial on how to solve for Mach numbers. Step by step tutorial including several examples of how to solve for Mach numbers for reference.
Overview
A Mach number is the speed of an object moving through the air, or any fluid substance, divided by the speed of sound as it is in that substance. It is often used to represent an object such as an aircraft or a missile’s speed, when it is travelling at the speed of sound or multiples of the speed of sound. This can be portrayed mathematically in the equation M = vs / u, where M is the Mach number, vs is the speed of the source (the object relative to the medium), and u is the speed of sound in the medium.
