This is a characterization of faith. Is it a definition as well? Not every characterization of a thing is a definition of it. E.g., when I say that grass is green and eaten by cows, I am accurately describing grass, but not defining it.
Now faith is the assurance of things hoped for, the conviction of things not seen.
“the assurance of things hoped for"
If it is, then it seems paradoxical: If I am sure, then I am not hoping. If I am hoping, then I am not sure.
(Consider the difference between wishing, hoping, and believing: I don't need any evidence in order to wish for something. I have not bought a lottery ticket, but I can still wish I were going to win, even though I know I can't. In contrast, to hope requires that I have some evidence, at least enough to believe what I hope for is possible. If I have bought a ticket in the lottery, then I can hope that I win, even if the odds against against my winning are very long. However, when I see that my number has been drawn and I get the official notification from the state lottery commission, I now believe--I'm sure--that I have won, and I no longer hope that I have won. So combining being sure with hoping is surprising.)
How about
“the conviction of things not seen...”
First: should the “not seen” be taken literally, or as a way to say “things not observed?”
But reading "things not seen" as "things not observed" still seems to include way too much. There are lots of things I cannot see, hear, smell, feel, or taste that I believe exist but that belief is not a matter of faith. E.g., I cannot observe atoms or radio waves but my belief that there are such things is not a matter of faith. Defining faith as belief in the unobservable still seems to include far too much.
I A person has faith = she has a belief in something she cannot see
II A person has faith = she has a belief in something she cannot observe
III A person has faith = she has a belief that she cannot justify
The author of the epsitle to the Hebrews must have had something more interesting in mind!