Difference between Orthogonal and Orthonormal
Difference between Orthogonal and Orthonormal

Difference between Orthogonal and Orthonormal

In the field of mathematics, two terms orthogonal and orthonormal are as often as possible utilized alongside a set of vectors. Here, the expression “vector” is utilized as a part of the feeling that it is a component of a vector space as an algebraic arrangement utilized as a part in linear algebra. To make it understandable for you, we are going to consider an inner product space as vector space V alongside an inward item [ ] characterized on V.


In field of mathematics, mainly linear algebra, an orthogonal premise for an internal item space V is a premise for V whose vectors are commonly orthogonal. On the off chance that the vectors of an orthogonal premise are normalized, the subsequent premise is an orthonormal premise.


In mathematics field, especially linear algebra, an orthonormal premise for an inward item space V with limited measurement is a premise for V whose vectors can be said as orthonormal, actually, they represent all unit vectors and they are orthogonal to one another.

Orthogonal VS Orthonormal

In this article we are going to discuss some contrasts between orthogonal and orthonormal so that you can get a clear picture about these terms.

  • Definition:

When an inner product space V have non empty subset”S” then it can be said as orthogonal, if and if for each discrete u, v present in S as [u, v] = 0.

Be that as it may, it is said to be orthonormal, if and just if an extra condition that is for every vector u present in S as [u, u] = 1 is fulfilled.

  • Said as:

Any orthogonal set cannot be said as orthonormal.

Any orthonormal set can be said as orthogonal.

  • Relates:

Any orthogonal set relates to an exceptional orthonormal set

An orthonormal set may compare to numerous orthogonal sets.


From the above article we can conclude that orthonormal sets can be declared as orthogonal but not in case of orthogonal.