Orthogonal set - Geometric interpretation

  • #1
Orthogonal set -- Geometric interpretation

Hello,

If we have two vectors u,v then in an inner product space, they are said to be orthogonal if <u,v>=0.

Well, orthogonal means perpendicular in Euclidean space, i.e. 90 degrees. How <u,v> becomes zero.

Secondly, if I have three vectors, v1,v2,v3 with certain values, computing, we get <v1,v2>=0
<v1,v3>=0
<v2,v3>=0

How will it look like in geometrical figure. I mean to say, what if we take these 3 vectors and put it on a picture and how it would look like?

Thanks,

-- Shounak
 

Answers and Replies

  • #2
Erland
Science Advisor
738
136


Hello,

If we have two vectors u,v then in an inner product space, they are said to be orthogonal if <u,v>=0.

Well, orthogonal means perpendicular in Euclidean space, i.e. 90 degrees. How <u,v> becomes zero.

Secondly, if I have three vectors, v1,v2,v3 with certain values, computing, we get <v1,v2>=0
<v1,v3>=0
<v2,v3>=0

How will it look like in geometrical figure. I mean to say, what if we take these 3 vectors and put it on a picture and how it would look like?

Thanks,

-- Shounak
In R3, these will be three perpendicular vectors. For example, the standard basis vectors (1,0,0), (0,1,0), and (0,0,1).
In R2, this is not possible, unless at least one of the vectors is the zero vector.
 

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