With all due respect, that strikes me as a very odd, and inadequate, definition.

As has been noted, faith is the substance of things hoped for, the evidence of things not seen (Heb. 11:1). Our actions, except when performed in private, are seen. And even the private ones - - - oh, me - - - are seen by God.

But faith cannot be defined in one verse alone. We mustn't forget the provenace of faith: For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast (Eph. 2:8,9). In verse 8, the antecedent of "and that" is faith: faith is the gift of God. It is certainly not my acts, or anything generated by my acts.

Of course, this God-given faith will result in actions: that's what the very next verse is about: For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them. But that's a far different thing than saying that faith is "the action that reveals what you believe and who you are."

Yes, my "good works," such as they are, might reveal what I believe in; or they might not. They might be misinterpreted. One of the great horrors of my life is the fear that unbelievers might say, "Oh, he did good things because he was a good man, or a nice guy." God forbid!

If you want to see the acts that reveal "who I am," look at my sins. I'm just a forgiven sinner.