Thats probably sounds really simple but i cant figured out. was tring for few days.

Thats probably sounds really simple but i cant figured out... was tring for few days...see if my covariance matrix is positive definite, how can I prove that the coefficient of the first principal component are all of the same sign and coefficient of each other principal component cannot be all of the same sign?I try to prove from the definition but cant get the idea... can any one help?Thanks