Need a bit more information about second-order tensors

[Vectronix]

I am aware that a vector is a first-order tensor, and that a second-order tensor has nine components in three-space, but can someone tell me more about the directional quantities that are associated with these nine components? Are they still unit vectors? Can a second order tensor be written as a linear combination of its components and these directional quantities? Is it true that the product of a second-order tensor and a vector is a vector? If so, then why?

 

[Vectronix]

hey, whoever turned the word 'tensor' in my post to a link, thank you. I will examine this definition as well as some other information that I have found, as these seem to be helpful in getting me the info I was looking for. So, unless someone else has anything to add, nevermind. :) Thanks!