It all depends what you want to do with it. A very basic system could run on the following,
CPU - i386@33Mhz
Memory - about 4mb is the minimum I think, maybe even 2mb
HD size - You don't even need a HD, I could fit on a 1.44 floppy disk
Display - Almost anything, depends on the hardware to drive it.
Input - minimum basic would be a keyboard, only really need to configure it.
I think that about sums up minimum hardware needed. But then if i is going to be som sort of device that does not need any interaction then the display or keyboard would not be needed.
What you really need to find out is what sort of system do you need to run.
edit:
Also what do they mean by linux v2.6. After all that is just the kernel, it is not an entire OS