Question

Difference between orthogonality and orthonormality

Answer 1

 Euclidean geometry, orthogonalobjects are related by their perpendicularity to one another. Lines or line segments that are perpendicular at their point of intersection are said be related orthogonally. Similarly, two vectors are considered orthogonal if they form a 90-degree angle.

In linear algebra, two vectors in an inner product space are orthonormal, if they are orthogonal and unit vectors. A set of vectors form an orthonormalset, if all vectors in the set are mutually orthogonal and all of unit length. Anorthonormal set which forms a basis is called an orthonormal basis.