20: Vector Spaces
In a physical system a quantity can often be described with a single number. For example, we need to know only a single number to describe temperature, mass, or volume. However, for some quantities, such as location, we need several numbers. To give the location of a point in space, we need \(x\text{,}\) \(y\text{,}\) and \(z\) coordinates. Temperature distribution over a solid object requires four numbers: three to identify each point within the object and a fourth to describe the temperature at that point. Often \(n\)-tuples of numbers, or vectors, also have certain algebraic properties, such as addition or scalar multiplication.