Do you know what an eigen value is?
"This sentence has five words."
That's an eigen value. It's a self-defining entity. Its outputs are identical to itself.
If I were to say instead, "This sentence has a lot of words and syllables," that would not be an eigen value because it's subjective. We can debate what "a lot" is or isn't. And that difference is important.
Want to see how an eigen value plays out in real life? Look at Vibram and its FiveFingers shoe.
Vibram USA's CEO, Tony Post, had a seemingly insurmountable problem: How do you breathe innovation into a commodity business that frankly doesn't have too many moving parts (no moving parts to be precise)? Vibram makes soles for other manufacturers' shoes.
The company pushed hard into its well-developed OEM [original equipment manufacturer] space, branding its soles with its trademark yellow tab, and considered how to dip a proverbial toe into the athletic-shoe market.
At the same time, Post was dealing with a seemingly insurmountable problem of his own: As a competitive runner coming off potentially career-ending knee surgery, he was looking for a solution to the chronic knee pain that plagues runners after a lifetime of training.