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During his career, Hoover was awarded the following military medals: the Distinguished Flying Cross, the Soldier's Medal for non-combat valor, the Air Medal with several oak leaf clusters, the Purple Heart and the French Croix de Guerre. He was also made an honorary member of the United States Navy aerobatic team the Blue Angels, the United States Air Force Thunderbirds, the Canadian Forces Snowbirds, the American Fighter Aces Association and the original Eagle Squadron, and received an Award of Merit from the American Fighter Pilots Association. He was inducted into the National Aviation Hall of Fame in 1988 and to the Aerospace Walk of Honor in 1992.