as a matter of fact is an adverb meaning "in reality or actuality". It carries one recorded sense.
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”
Definitions, synonyms and semantic relations for as a matter of fact come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.