# Is a set of orthogonal basis vectors for a subspace unique?

Gold Member
Homework Statement
Is a set of orthogonal basis vectors for a subspace unique?

The attempt at a solution
I don't know what this means. Can someone please explain?
I managed to find the orthogonal basis vectors and afterwards determining the orthonormal basis vectors, but i'm not sure what the question is asking for exactly?

## Answers and Replies

LCKurtz
Homework Helper
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Unique means only one. So, for example, in R2, (1,0) and (0,1) are an orthogonal basis. Can you find a different pair giving an orthogonal bases for R2?

Gold Member
Unique means only one. So, for example, in R2, (1,0) and (0,1) are an orthogonal basis. Can you find a different pair giving an orthogonal bases for R2?
Thanks for your time, LCKurtz.
To answer your question... Yes, (0,-1) and (-1,0) as well as the following pair (0,0) and (-1,0) and others, like (-1,0) and (0,2), etc.
But what is your point? I don't see how that answers my original question.

LCKurtz
Homework Helper
Gold Member
Thanks for your time, LCKurtz.
To answer your question... Yes, (0,-1) and (-1,0) as well as the following pair (0,0) and (-1,0) and others, like (-1,0) and (0,2), etc.
But what is your point? I don't see how that answers my original question.

You don't?? Your question was whether a subspace had a unique (meaning only one) set of basis vectors. You have just mentioned several. And you could find entirely different ones by rotating them too.

Gold Member
OK, i missed that point, as my mind was focused more on the actual orthogonal basis vectors, which is a 3x3 matrix, which i assume would not be unique either. Thanks!