- 21st April 2009, 16:49 #1

- Join Date
- Oct 2008
- Location
- Sindh, Pakistan
- Posts
- 896
- Helped
- 178 / 178
- Points
- 9,408
- Level
- 23

## 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

- 21st April 2009, 16:49

- 21st April 2009, 22:58 #2

- Join Date
- Apr 2009
- Posts
- 12
- Helped
- 2 / 2
- Points
- 790
- Level
- 6

## orthogonal and orthonormal signals

orthogonal as u said

but orthonormal is orthogonal and normalized at same time

1 members found this post helpful.

- 22nd April 2009, 05:36 #3

- Join Date
- Oct 2008
- Location
- Sindh, Pakistan
- Posts
- 896
- Helped
- 178 / 178
- Points
- 9,408
- Level
- 23

## orthogonal perpendicular difference

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

- 22nd April 2009, 06:50 #4

- Join Date
- Feb 2009
- Posts
- 10
- Helped
- 2 / 2
- Points
- 1,127
- Level
- 7

## 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.

1 members found this post helpful.

- 22nd April 2009, 06:50

- 22nd April 2009, 16:24 #5

- Join Date
- Oct 2008
- Location
- Sindh, Pakistan
- Posts
- 896
- Helped
- 178 / 178
- Points
- 9,408
- Level
- 23

## 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

- 22nd April 2009, 16:38 #6

- Join Date
- Feb 2009
- Posts
- 10
- Helped
- 2 / 2
- Points
- 1,127
- Level
- 7

## 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"?

- 22nd April 2009, 18:00 #7

- Join Date
- Apr 2009
- Posts
- 12
- Helped
- 2 / 2
- Points
- 790
- Level
- 6

## 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-

- 24th April 2009, 18:18 #8

- Join Date
- Jul 2006
- Location
- Bahrain
- Posts
- 182
- Helped
- 69 / 69
- Points
- 3,351
- Level
- 13

## orthogonal and orthonormal functions

Hi,

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

Regards

- 6th December 2014, 08:32 #9

- Join Date
- Mar 2014
- Posts
- 4
- Helped
- 0 / 0
- Points
- 158
- Level
- 2

## 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.