ABSTRACT
Every Hilbert space gives a means by which functions can be regarded as points in an infinite-dimensional space. The utility of this geometric perspective is found in our ability to generalize the notions of a length, orthogonality, and linear combinations of elements from elementary linear algebra to more abstract mathematical spaces. The key concept that governs this geometric perspective is a basis of the spaces. In the beginning of this chapter, we review the essential properties of a basis specifically in an infinite-dimensional space.
