Granta Posted December 14, 2004 Report Share Posted December 14, 2004 Hi everyone, I was browsing the internet looking for somw opinions on a question I have and found this place. I though it might be a good place to ask for some educated help!! Anyway, here is my questions: If I have an n*m matrix X made up of n measurements of m variables (assuming all the variables measure temperature and so the units are Kelvin (K)). Does this imply that the covariance of X has units K^2? Also, if S = covariance(X) and S = ULU' (singular value decomposition), what are the units of U, L and U'?? Thanks for your help,Granta Link to comment Share on other sites More sharing options...
Tormod Posted December 14, 2004 Report Share Posted December 14, 2004 Welcome, Granta. Bo is our maths expert, I am sure he will help you out as soon as he logs on. Link to comment Share on other sites More sharing options...
Bo Posted December 16, 2004 Report Share Posted December 16, 2004 hi and welcome to this fora! If I have an n*m matrix X made up of n measurements of m variables (assuming all the variables measure temperature and so the units are Kelvin (K)). Does this imply that the covariance of X has units K^2? yes; just look at the definition of covariance, and you'll see that the elements occur squared. Also, if S = covariance(X) and S = ULU' (singular value decomposition), what are the units of U, L and U'??[/Quote] Since the matrices U and U' need to obey: U Ut = U't U' = 1, (t denotes the transposed matrix) they have to be unitless; So L has the same units as S. Bo Link to comment Share on other sites More sharing options...
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