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As a matter of fact vs Fact of the matter is

as a matter of factas it happens; actually:

  • As a matter of fact, I recently found two small stories that provoked more thought than the other articles I read.

Note: The expression does not correlate in meaning with the phrase as a matter of course—as part of a standard procedure; as smth. that one expects automatically to happen:

  • Medical insurance is provided for students by the Institute as a matter of course.

fact of the matter is, thethe essential or important thing is:

  • The fact of the matter is that she only married me because Zeeman wouldn’t get a divorce, and she was punishing him.