👉 In mathematics and physics, an orthonormal set is a set of vectors that are orthogonal to each other. This means that they have the same length (or magnitude) but point in opposite directions. Orthonormal sets are often used in Fourier analysis and quantum mechanics to represent states. An orthonormal basis is a specific kind of orthonormal set, where all the elements of the set are mutually orthogonal. If you want to find an orthonormal basis for a particular space (e