MrA Posted November 9, 2004 Share Posted November 9, 2004 I need a little help on my math assignment (as you can probably tell). Please note that I do not want the answer. I just need a pointer or two on how to approach the problem. I've tried to put the problem into words since a couple of the symbols nescessary to properly show the problem can not be displayed. I've also attached the assignment sheet. The problem is 6b. For V is a 3-D complex vector space, let W = span {(1,0,i), (1,2,1)} Find a basis for the orthogonal complement of W. Thanks in advance. m235assign8f04.pdf Link to comment Share on other sites More sharing options...
rumbleph1$h Posted November 10, 2004 Share Posted November 10, 2004 Well a start would be recognizing that: vectors a and b are orthogonal when a ∙ b = 0 ;) EDIT: okay , just looked at the attached file and now i'm way confused...... :cry: Link to comment Share on other sites More sharing options...
MrA Posted November 10, 2004 Author Share Posted November 10, 2004 Well a start would be recognizing that:vectors a and b are orthogonal when a ∙ b = 0 ;) 584895735[/snapback] I kinda knew that. Doesn't help me to find the orthogonal complement. I was thinking of using the cross product since that gives a vector orthogonal to the other two. The problem is that this is the complex vector space and I don't think that one vector will suffice as the orthogonal complement. Had this been a real vector space, I would have just had to do the cross product, easy as pi. EDIT: okay , just looked at the attached file and now i'm way confused...... It's OK to be confused. For me, this is second year university. (It is first year for science students, but us mathies have to take an additional course in classical algebra which holds back this course) Link to comment Share on other sites More sharing options...
rumbleph1$h Posted November 10, 2004 Share Posted November 10, 2004 It's OK to be confused. For me, this is second year university. (It is first year for science students, but us mathies have to take an additional course in classical algebra which holds back this course) 584895764[/snapback] :rofl: , I apologize. I thought this was a simple vector problem. I have not yet taken Linear Algebra (only at Calc 3 right now)... so wish I could help you out. by the way, is 'orthonormal' the same as 'orthogonal' or perpendicular? :huh: Link to comment Share on other sites More sharing options...
MrA Posted November 10, 2004 Author Share Posted November 10, 2004 :rofl: , I apologize. I thought this was a simple vector problem. I have not yet taken Linear Algebra (only at Calc 3 right now)... so wish I could help you out. by the way, is 'orthonormal' the same as 'orthogonal' or perpendicular? :huh: 584895819[/snapback] Only at calc 3? I'm taking a calc 3 course and lin alg (and electricity & magnetism which is mostly vector calc). Shouldn't you be taking Calc & linear algebra at the same time since they're two distinct braches of math and the two most important ones. Anywho, orthogonal and orthonormal are almost the same. Orthogonal means perpendicular when you're talking about a real 2 or 3-D space (I'm sure you knew this). When you're talking about 4-D or higher or non-real spaces (such as complex spaces), the term perpendicular doesn't quite fit. Orthonormal mean orthogonal with a norm (length) of 1. Link to comment Share on other sites More sharing options...
rumbleph1$h Posted November 10, 2004 Share Posted November 10, 2004 Only at calc 3? I'm taking a calc 3 course and lin alg (and electricity & magnetism which is mostly vector calc). Shouldn't you be taking Calc & linear algebra at the same time since they're two distinct braches of math and the two most important ones. 584895989[/snapback] Probably..... makes sense to me. The recommended track at my university is the Calc series > Diff EQ > Linear Algebra > Advanced Engineering mathematics series Anyways, sorry for the thread hijack, and thanks for the 'orthonormal' clarification. :) Link to comment Share on other sites More sharing options...
MrA Posted November 10, 2004 Author Share Posted November 10, 2004 Probably..... makes sense to me. The recommended track at my university is the Calc series > Diff EQ > Linear Algebra > Advanced Engineering mathematics seriesAnyways, sorry for the thread hijack, and thanks for the 'orthonormal' clarification. :) 584896040[/snapback] It's ok. And you're welcome. You'll be learning all this fairly soon and then you'll feel like ripping the hair off your head. I'm tired. Me go sleep. Link to comment Share on other sites More sharing options...
ECEGatorTuro Posted November 10, 2004 Share Posted November 10, 2004 Hey, if you still need help, I can talk to my friend who is a statistics/math major taht is graduating. He is really good at all this stuff... ;) Let me know and I'll give him the thread link! Link to comment Share on other sites More sharing options...
MrA Posted November 10, 2004 Author Share Posted November 10, 2004 Hey, if you still need help, I can talk to my friend who is a statistics/math major taht is graduating. He is really good at all this stuff... ;) Let me know and I'll give him the thread link! 584896184[/snapback] Thanks. That'll be great. The assignment's officially due at midnight so I have plenty of time. I'll be asking around as well so I might have the answer before anyone else replies with it. Link to comment Share on other sites More sharing options...
faberoo Posted November 18, 2004 Share Posted November 18, 2004 hello sorry this is way past your hw deadline but if you're still wondering how to do it, you know that if you take the inner product of the two vectors spanning the basis for W, you need vectors that will give you 0 when you take the inner products of those to the W basis vectors. so i.e. find the null space for the row vectors of W. Link to comment Share on other sites More sharing options...
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