Maths question

[Granta]

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

[Tormod]

Welcome, Granta.

 

Bo is our maths expert, I am sure he will help you out as soon as he logs on.

[Bo]

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