Orthonormal Basis

An orthonormal basis is a powerful structure in linear algebra because it provides both theoretical simplicity and numerical stability. The basis vectors are mutually perpendicular and each has unit length. This makes projections, transformations, and coordinate calculations much cleaner. Orthonormal structures are highly important in PCA, Fourier analysis, quantum mechanics, and many signal processing applications. In machine learning, they are especially valuable for separating information components and building more interpretable representations.