Lindsey died after she was bitten by sharks while snorkeling with her family, according to Paul Rolle, deputy commissioner for the Royal Bahamas Police Force.
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Three sharks were involved. Officials said they bit her in the arms, legs and buttocks, and severed her right arm.
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Family members, including her parents, were with her during the snorkeling expedition near Rose Island around 2 p.m.
Family members saw the sharks and yelled a warning, but she didn't hear them in time.
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She was brought to a local hospital, where she was pronounced dead.
"Jordan was 21 and such a great daughter and person," Jordan's father, Michael Lindsey, said in a statement to ABC News. "We already miss her terribly."
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Her younger sister, Madison Lindsey, has started a GoFundMe page to help the family with funeral costs and transporting her body back to California.
"Jordan Lindsey was a beloved daughter, sister, girlfriend, and friend," the GoFundMe page said. "On June 26, 2019 Jordan was tragically killed from a shark attack in the Bahamas."
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"Jordan had the most beautiful, gentle soul and she will be missed deeply."
The young woman was also a student at Loyola Marymount University.
Officials with the Bahamas government said: "The Ministry of Tourism, on behalf of the Government and the people of The Bahamas expresses its condolences and deepest sympathies to the family and loved ones of the victim of Wednesday's shark attack off Rose Island, near New Providence."
The U.S. Embassy is working to bring her body back to California.
ABC News contributed to this report.