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Matheson was born on 8 February 1861 in Mayfair, London, England. He was the son of Alexander Matheson and his third wife Eleanor (née Perceval). His maternal grandfather was Spencer Perceval junior, his mother being a granddaughter of the assassinated British prime minister Spencer Perceval. Matheson's father, a Scotsman from Ross-shire, was a wealthy businessman and Liberal MP who was created a baronet in 1882.