| [ KAIST ] in KIDS 글 쓴 이(By): mkjung (루돌프아지) 날 짜 (Date): 2000년 12월 12일 화요일 오전 10시 32분 17초 제 목(Title): Re: [질문]canonical angle이 무엇인가요? what is canonical angle? ========== i guess i am the only person who can answer this question definitely although it is the first time hearing it. :) canonical expansion, canonical something in mathematics and statistics mean you have 'the' most important expansion or something. (most of the time it is related to basis expansion or orthonormal expansion. sometimes you have canonical coordinate system in Euler-Lagrangian mechanical system.) so my guess is that you expand your vector space A and B in terms of orthonormal basis a_1, a_2... a_m (for A with dim(A)=m ) and b_1, b_2...b_n (for B with dim(B)=n). Then my obvious guess is that the canonical angles are \theta_{ij} = cos^{-1} <a_i,b_j> where < , > is an inner product defined on the vector spaces A and B. what is canonical variate analysis? ===================== again this is the first time i am hearing this terminology. but it is easy to guess isn't it? :) it is the analysis based on these canonical coefficients. \theta_{ij} forms covariant 2nd order tensor and i am sure this is about 'statistical' analysis and these covariates. if you assume some 'stochastic' model on these covariates. you can estimate the expectation E \thetat_{ij}. Then a singular matrix (if m \neq n) C defined by C = (E \theta_{ij}) will completely determine the correlation structure between these two 'random vector spaces'. hmmmm.... 'random vector spaces'? this is a neat idea for ph.d. thesis !!!!! if anyone want to get ph.d. in statistics under my supervision, send me e-mail. kiki.... 키즈깡패단 단장 본협회에가입하실분은연락바떰� 하는일 키즈의 추접떠는 죽돌이들청소 titipas@earthlink.net |