Wiktionary
as a matter of fact
adv. (lb en modal) actually, in fact.
WordNet
as a matter of fact
adv. in reality or actuality; "in fact, it was a wonder anyone survived"; "painters who are in fact anything but unsophisticated"; "as a matter of fact, he is several inches taller than his father" [syn: in fact, in point of fact]
Usage examples of "as a matter of fact".
I didn't have to see the broken tail-light and the scratch up the driver's side to know that, but as a matter of fact I could see both.