I was reading Turk and Pentland paper 'Eigenfaces for recognition' and they assert that, if M < N, the maximum rank of a covariance matrix is M - 1, being M the number of samples and NxN the size of the covariance matrix.(adsbygoogle = window.adsbygoogle || []).push({});

Is there any simple demonstration of this fact?

Thanks in advance,

Federico

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Rank of sample covariance matrix

**Physics Forums | Science Articles, Homework Help, Discussion**