Difference between Orthogonal and Orthonormal?

[Communications_Engineer]

difference between orthogonal and orthonormal

Hey, I have a question, what is the difference between Orthogonal and Orthonormal?

Do they mean same thing? Like the inner product is equal to zero

 

[Etsh]

orthogonal and orthonormal signals

orthogonal as u said

but orthonormal is orthogonal and normalized at same time

 

[Communications_Engineer]

orthogonal perpendicular difference

please elaborate. what do you mean by "orthogonal & normailized at the same time"

 

[Moshu95]

orthogonal mean the same as orthonormal

Orthogonal mean that the dot product is null.
Orthonormal mean that the dot product is null and the norm is equal to 1.

If two or more vectors are orthonormal they are also orthogonal but the inverse is not true.

 

[Communications_Engineer]

difference orthogonal orthonormal

what is "norm" what are its benefits?

I've seen it being used many time in place of square of a vector of variables

 

[Moshu95]

convert orthogonal to orthonormal function

norm(u) is defined by <u,u> where <,> is a dot product and u a vector.
A norm depends on the dot product you chose to use.

What do you mean by "the benefits of the norm"?

 

[Etsh]

difference between orthorgonal and orthonormal

first the using of orthonormal as basis functions so it should be normalized

and when we do dot product of two orthogonal functions the result is zero

but when we do dot product for orthogonal function with itself the result will be constant or 1 if they normalized

so it is easier to use orthonormal from beginning to simplify the computations

refer to signal space
when we use orthonormal functions as basis functions so the amplitude of signal is square root of signal -will get the meaningful representation of signal -in direction of this basis

and for any other signal,u need to get the projection in this basis u need to get ratio between two amplitudes -signal and basis function if the basis function is not normalized-

 

[ahmedseu]

orthogonal and orthonormal functions

Hi,

Orthonormal means orthogonal (perpendicular) and the length of that vector equals to one.

Regards

 

[priteshmetha]

Re: difference between orthogonal and orthonormal

• A nonempty subset S of an inner product space V is said to
be orthogonal, if and only if for each distinct u, v in S, [u, v] = 0. However, it is orthonormal, if and only if an additional condition – for each vector u in S, [u, u] = 1 is satisfied.
• Any orthonormal set is orthogonal but not vice-versa.
• Any orthogonal set corresponds to a unique orthonormal set but an orthonormal set may correspond to many orthogonal sets.