L.A. Clippers star Matt Barnes has separated from his reality star wife Gloria Govan ... TMZ Sports has learned -- and sources close to the couple tell us it's all over "trust issues."

Barnes and Govan were married back in 2012 -- and have 5-year-old twin boys together. 

Sources connected to the couple tell us Matt and "Basketball Wives: LA" star Gloria have been separated for about 6 weeks. 

We're told they're still technically living in the same house -- but it's just temporary and it's just a matter of time before one of them moves out and they start the divorce process. 

Maybe one of the biggest signs things were going south ... Matt hasn't posted a picture of Gloria on Instagram in months. And we haven't been able to find a picture of Gloria wearing her wedding ring since late-August.