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

1. Sep 24, 2011

### sharks

The problem statement, all variables and given/known data
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?

2. Sep 24, 2011

### LCKurtz

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?

3. Sep 24, 2011

### sharks

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.

4. Sep 24, 2011

### LCKurtz

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.

5. Sep 24, 2011

### sharks

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!