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The appointment follows her direction of the orchestra in two recent concerts which received rave reviews from music critics.
Dr Mathieson (34) said the appointment was for the next four years, and she was delighted to be ''cementing'' her relationship with NYOS.
Dr Mathieson said the orchestra was for ambitious young musicians aged between 8 and 15, and was the first step the path for aspiring members of the NYOS Senior Orchestra and Symphony Orchestra (the National Youth Orchestra of Scotland).
The Junior Orchestra provides younger pupils with the opportunity to perform large scale symphonic repertoire at top class venues.
Her work with the orchestra so far has won over music critics, including The Herald Scotland's Michael Tumelty, who gave Dr Mathieson and the NYOS Junior Orchestra a five star review following their performance at Greyfriars Kirk in Edinburgh recently.
''Everything they did, guided and released by the charismatic New Zealand conductor Holly Mathieson, from MacCunn's Land of the Mountain and Flood to Gliere's little known, gloriously melodic Horn Concerto, came soaring off the page.''
Dr Mathieson recently held one of the world's most coveted fellowships for emerging conductors - she was the Royal Conservatoire of Scotland (Glasgow) Leverhulme Conducting Fellow, which had allowed her to work with the BBC Scottish Symphony Orchestra, the Royal Scottish National Orchestra, and the Red Note Ensemble.
At the moment, she is making her debut as associate conductor of Opera Holland Park, conducting the Christine Collins Young Artist performance of Delibes' Lakme.