Holdsworth died on Sunday, according to a Facebook post by his daughter Louise.
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Born in Bradford, England, Holdsworth had lived in Southern California for several decades. His complex guitar work was cited as an influence by musicians such as Eddie Van Halen and Robben Ford.
Holdsworth started out playing with rock and jazz fusion bands in the early 1970s and then joined up with acts from the Canterbury progressive scene, including Soft Machine and Pierre Moerlen's Gong.
He played with bassist Stanley Clarke, King Crimson drummer Bill Bruford's solo act, and with violinist Jean-Luc Ponty's band, and was then recruited to join progressive supergroup U.K. with Bruford, violinist Eddie Jobson, and bassist John Wetton.
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From the 1980s onward, Holdsworth released a number of jazz fusion solo albums with collaborators including Gordon Beck and Mark Varney, and continued to tour. Road Games, from 1983, received a Grammy nomination for best rock instrumental performance.
Musicians including Joe Satriani mourned Holdsworth on Twitter.
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