You are Here: Home >< Maths

# Explain how i and j notation works please? watch

1. (Original post by drandy76)
And the I denotes which unit vector it denotes right, so e_3 would be equivalent to k?

Posted from TSR Mobile
Yep
2. (Original post by drandy76)
From what I recall they're components? I'll check tomorrow and get back to you but I recall reading about them to show why vector addition works

Posted from TSR Mobile
Yeah, that's what I said, the components are all perpendicular (orthogonal) to one another and form an orthonormal basis.
3. (Original post by Zacken)
Yeah, that's what I said, the components are all perpendicular (orthogonal) to one another and form an orthonormal basis.
Are orthonormal basis' restricted to just 3 vectors or is it any set of vectors which are orthogonal to one another?

Posted from TSR Mobile
4. (Original post by drandy76)
Are orthonormal basis' restricted to just 3 vectors or is it any set of vectors which are orthogonal to one another?

Posted from TSR Mobile
The set forms an orthonormal basis, so definitely not just 3 vectors. That would ruin the whole point of studying vector spaces.
5. (Original post by Zacken)
The set forms an orthonormal basis, so definitely not just 3 vectors. That would ruin the whole point of studying vector spaces.
oh i see, so the restriction is based upon the which space you're working in? so for example R^5 space would be restricted to no more than 5 unit vectors forming an orthonormal basis?
6. (Original post by drandy76)
oh i see, so the restriction is based upon the which space you're working in? so for example R^5 space would be restricted to no more than 5 unit vectors forming an orthonormal basis?
I'm not sure. So I'll let someone else step in, Rayquaza and clear it up. But I think that 5 unit vectors (linearly independent) would span the space . I'm not sure if you can have an orthonormal basis for a space with but I really don't know so I'm not going to say anything about it.
7. (Original post by Zacken)
I'm not sure. So I'll let someone else step in, Rayquaza and clear it up. But I think that 5 unit vectors (linearly independent) would span the space . I'm not sure if you can have an orthonormal basis for a space with but I really don't know so I'm not going to say anything about it.
Tried to google it but all i got were paragraphs about orientations in Euclidean space
8. i'm surprised this thread is still going xD
9. (Original post by drandy76)
oh i see, so the restriction is based upon the which space you're working in? so for example R^5 space would be restricted to no more than 5 unit vectors forming an orthonormal basis?
Hmm linear algebra isn't my best area of maths! But yeah I think R^5 would need 5 vectors to form the basis. But they don't need to be ones like (1,0,0,0,0), (0,1,0,0,0),etc you can have other weird ones as long as they are linearly independent.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 6, 2016
Today on TSR

### A-Level OCR Biology Unofficial Markscheme

Find out how you've done here

### 1,293

students online now

Exam discussions

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams