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From: atanas on 24 Apr 2010 18:47 Hello, I have problem for my project: Let we matrices C0,C1,C2,C3,D0,D1,D2, and D3 are with size 2x2. We knowing matrices C0,C1,C2,and C3 that [C0 C1 C2 C3]*[C0 C1 C2 C3]'=I We construct the matrix W=[C0 C1 C2 C3 zeros(2,2) zeros(2,2); zeros(2,2) zeros(2,2) C0 C1 C2 C3; D0 D1 D2 D3 zeros(2,2) zeros(2,2); zeros(2,2) zeros(2,2) D0 D1 D2 D3]. How to find matrix D0,D1,D2, and D3 so that satisfy condition W*W'=I?
From: Roger Stafford on 25 Apr 2010 01:58 "atanas " <atanaslove2000(a)abv.bg> wrote in message <hqvsda$m6d$1(a)fred.mathworks.com>... > Hello, > I have problem for my project: > Let we matrices C0,C1,C2,C3,D0,D1,D2, and D3 are with size 2x2. > We knowing matrices C0,C1,C2,and C3 that > [C0 C1 C2 C3]*[C0 C1 C2 C3]'=I > We construct the matrix > W=[C0 C1 C2 C3 zeros(2,2) zeros(2,2); > zeros(2,2) zeros(2,2) C0 C1 C2 C3; > D0 D1 D2 D3 zeros(2,2) zeros(2,2); > zeros(2,2) zeros(2,2) D0 D1 D2 D3]. > > How to find matrix D0,D1,D2, and D3 so that satisfy condition W*W'=I? ------------ If I understand what you are saying correctly, that makes a nice problem which can readily be solved using matlab. In general, there will be one degree of freedom in the choice of the D quantities. However, it sounds very much like a student homework assignment. CSSM people usually follow the policy of not giving assistance in such cases except to help with tentative matlab coding that has already been developed by the student. I suggest you ponder over this problem until you have a possible algorithm in mind and can show us your ideas about how it might be carried out in matlab. Then you might receive some help. Roger Stafford
From: atanas on 25 Apr 2010 09:40 "Roger Stafford" <ellieandrogerxyzzy(a)mindspring.com.invalid> wrote in message <hr0lld$511$1(a)fred.mathworks.com>... > "atanas " <atanaslove2000(a)abv.bg> wrote in message <hqvsda$m6d$1(a)fred.mathworks.com>... > > Hello, > > I have problem for my project: > > Let we matrices C0,C1,C2,C3,D0,D1,D2, and D3 are with size 2x2. > > We knowing matrices C0,C1,C2,and C3 that > > [C0 C1 C2 C3]*[C0 C1 C2 C3]'=I > > We construct the matrix > > W=[C0 C1 C2 C3 zeros(2,2) zeros(2,2); > > zeros(2,2) zeros(2,2) C0 C1 C2 C3; > > D0 D1 D2 D3 zeros(2,2) zeros(2,2); > > zeros(2,2) zeros(2,2) D0 D1 D2 D3]. > > > > How to find matrix D0,D1,D2, and D3 so that satisfy condition W*W'=I? > ------------ > If I understand what you are saying correctly, that makes a nice problem which can readily be solved using matlab. In general, there will be one degree of freedom in the choice of the D quantities. > > However, it sounds very much like a student homework assignment. CSSM people usually follow the policy of not giving assistance in such cases except to help with tentative matlab coding that has already been developed by the student. I suggest you ponder over this problem until you have a possible algorithm in mind and can show us your ideas about how it might be carried out in matlab. Then you might receive some help. > > Roger Stafford I thing for this problem about 1 year! But impossible that is solved! Please give to hit to me, can be that by mail. Thank for your answer.
From: Roger Stafford on 25 Apr 2010 11:14 "atanas " <atanaslove2000(a)abv.bg> wrote in message <hr1gnq$esr$1(a)fred.mathworks.com>... > I thing for this problem about 1 year! But impossible that is solved! Please give to hit to me, can be that by mail. > Thank for your answer. -------- Let me ask you a question about this problem, Atanas. If my interpretation is correct, you stated only that you are given C's such that [C0 C1 C2 C3]*[C0 C1 C2 C3]' = I (1) (where presumably I is the 2 x 2 identity matrix, eye(2).) However, implicit in the final requirement that your W*W' = eye(8) is the constraint that V = [C0 C1 C2 C3 zeros(2,2) zeros(2,2); zeros(2,2) zeros(2,2) C0 C1 C2 C3] must satisfy V*V' = eye(4) (2) Although equation (2) does clearly imply equation (1), the reverse does not necessarily hold. Therefore you must really be assuming the stronger condition (2) for the C's in this problem. Is that true? If so, here is another question for you. Have you figured out how to generate examples of C's in matlab that would satisfy (2)? If you can do that, you may be well on your way to solving the whole problem. Roger Stafford
From: atanas on 25 Apr 2010 12:05
"Roger Stafford" <ellieandrogerxyzzy(a)mindspring.com.invalid> wrote in message <hr1m7t$46j$1(a)fred.mathworks.com>... > "atanas " <atanaslove2000(a)abv.bg> wrote in message <hr1gnq$esr$1(a)fred.mathworks.com>... > > I thing for this problem about 1 year! But impossible that is solved! Please give to hit to me, can be that by mail. > > Thank for your answer. > -------- > Let me ask you a question about this problem, Atanas. If my interpretation is correct, you stated only that you are given C's such that > > [C0 C1 C2 C3]*[C0 C1 C2 C3]' = I (1) > > (where presumably I is the 2 x 2 identity matrix, eye(2).) However, implicit in the final requirement that your W*W' = eye(8) is the constraint that > > V = [C0 C1 C2 C3 zeros(2,2) zeros(2,2); > zeros(2,2) zeros(2,2) C0 C1 C2 C3] > > must satisfy > > V*V' = eye(4) (2) > > Although equation (2) does clearly imply equation (1), the reverse does not necessarily hold. Therefore you must really be assuming the stronger condition (2) for the C's in this problem. Is that true? > > If so, here is another question for you. Have you figured out how to generate examples of C's in matlab that would satisfy (2)? If you can do that, you may be well on your way to solving the whole problem. > > Roger Stafford > Sir Stafford, thank against. C's matrices are ready orhogonal. D's matrices need to find that Q = [D0 D1 D2 D3 zeros(2,2) zeros(2,2); zeros(2,2) zeros(2,2) D0 D1 D2 D3] must satisfy V*V'=eye(2); (condition 1) V*Q'=zeros(2); (condition 2) Q*V'=zeros(2); (condition 3) Q*Q'=eye(2); (condition 4). I have already only condition 1! Need to find conditions 2, 3 and 4. That all. Thanks for your help. |