Astronauts Thomas K. (Ken) Mattingly and Henry W. Hartsfield start work today on a three-week debriefing after their near-flawless week in orbit aboard the space shuttle Columbia. They relaxed at home yesterday, their first day off in many months.

The astronauts' return to Earth Sunday marked the fourth and final test flight of the shuttle, which is now cleared to begin operational flights.

Space agency officials said Columbia returned from its fourth flight in better shape than it did from earlier missions. They said only three small heat protection tiles came off during the flight.

The tiles, bonded on Columbia's hull to protect it from the heat of reentry into Earth's atmosphere, have been troublesome from the beginning of the shuttle development. "I think we've got the tile problem licked," said a space engineer, who asked that his name not be used.

The spacecraft will remain at Edwards Air Force Base in California for several days before being mounted atop a 747 transport for the trip to the Kennedy Space Center in Florida.

There, it will be refitted and prepared for a short flight scheduled for November.

Columbia's sister ship, Challenger, completed its 747 ride to Houston for an overnight stop en route to Florida.