Rex E. Alexander (June 1, 1924 – March 28, 1982) was a college basketball and tennis coach who was the head coach of the Murray State Racers from 1954 to 1958.
Alexander was born June 1, 1924 in Union County, Kentucky.
An assistant under Harlan Hodges, Alexander was promoted to head coach in 1954 after Hodges left MSU for Idaho and former North Carolina head coach Tom Scott turned down the job. In his four seasons at Murray State, Alexander had a 45–54 record and no tournament appearances. He was replaced by DePauw University head coach Cal Luther on March 5, 1958, but stayed on as an assistant coach and professor. In 1976 he was the recipient of the Murray State Distinguished Professor award. He was inducted into the Murray State Athletics Hall of Fame in 2000.
Alexander's son David played basketball at Western Kentucky in 1971. His grandson Troy played for Southern Methodist University.
He died in an automobile accident on March 28, 1982 at the age of 57 in Murray, Calloway County. He was buried in Murray City Cemetery.