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21st April 2009, 15:49 #1
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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, 15:49

21st April 2009, 21:58 #2
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orthogonal and orthonormal signals
orthogonal as u said
but orthonormal is orthogonal and normalized at same time
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22nd April 2009, 04:36 #3
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orthogonal perpendicular difference
please elaborate. what do you mean by "orthogonal & normailized at the same time"

22nd April 2009, 05:50 #4
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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.
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22nd April 2009, 05:50

22nd April 2009, 15:24 #5
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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, 15:38 #6
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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, 17:00 #7
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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

22nd April 2009, 17:00

24th April 2009, 17:18 #8
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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
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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 viceversa.
• Any orthogonal set corresponds to a unique orthonormal set but an orthonormal set may correspond to many orthogonal sets.
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