Orthonormalsystem
An orthonormal system is a set of vectors in an inner product space that are both orthogonal and normalized. Orthogonal means that the inner product of any two distinct vectors in the set is zero. Normalized means that the inner product of any vector with itself is one, which is equivalent to saying that each vector has a magnitude or length of one.
In simpler terms, an orthonormal system consists of "unit" vectors that are all mutually perpendicular. This
The concept of orthonormal systems is fundamental to Fourier analysis, where functions are represented as sums