Orthonormal basis

An orthonormal basis is a set of vectors in a space that are both perpendicular (orthogonal) to each other and of unit length (normalized). These vectors serve as building blocks for representing any point or vector in that space, similar to how coordinate axes (x, y, z) work in 3D space. Because they are orthogonal and normalized, calculations become simpler and more stable. This concept is fundamental in many areas like signal processing, mathematics, and physics, enabling efficient decomposition, analysis, and reconstruction of complex vectors or functions.