Hey there! Sign in to join this conversationNew here? Join for free
    • Community Assistant
    Offline

    17
    ReputationRep:
    Community Assistant
    (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
    Offline

    22
    ReputationRep:
    (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 i, j, k components are all perpendicular (orthogonal) to one another and form an orthonormal basis.
    Offline

    12
    ReputationRep:
    (Original post by Zacken)
    Yeah, that's what I said, the i, j, k 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
    Offline

    22
    ReputationRep:
    (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 \{e_1, e_2, \cdots, e_n\} forms an orthonormal basis, so definitely not just 3 vectors. That would ruin the whole point of studying vector spaces.
    Offline

    12
    ReputationRep:
    (Original post by Zacken)
    The set \{e_1, e_2, \cdots, e_n\} 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?
    Offline

    22
    ReputationRep:
    (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 \mathbb{R}^5. I'm not sure if you can have an orthonormal basis \{e_1, \cdots e_k\} for a space \mathbb{R}^n with k \neq n but I really don't know so I'm not going to say anything about it.
    Offline

    12
    ReputationRep:
    (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 \mathbb{R}^5. I'm not sure if you can have an orthonormal basis \{e_1, \cdots e_k\} for a space \mathbb{R}^n with k \neq n 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
    • Thread Starter
    Offline

    3
    ReputationRep:
    i'm surprised this thread is still going xD
    • Community Assistant
    Offline

    17
    ReputationRep:
    Community Assistant
    (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.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Have you ever participated in a Secret Santa?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.