There are several definitions of orthogonality:

  • Two Euclidean vectors are orthogonal if they are perpendicular, i.e., they form a right angle.
  • Two vectors, $\mathbf x$ and $\mathbf y$ are orthogonal if their Inner Product $\mathbf x^T \mathbf y = 0$ This relationship is denoted $\mathbf x \, \bot \, \mathbf y$: Vector Orthogonality
  • Two Vector Subspaces are orthogonal if each vector from one subspace is orthogonal to each vector of another subspace: Space Orthogonality
  • Two Functions are orthogonal if their inner product is 0: Orthogonal Functions