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The Seventh Linear Algebra Workshop (LAW'14) was held at Faculty of Mathematics and Physics, Ljubljana, Slovenia, June 4 - 12, 2014. The main theme of the workshop is the interplay between operator theory and algebra. The workshop follows the usual format. A few hours of talks are scheduled for the morning sessions, while afternoons are reserved for work in smaller groups. LAW'14 was organized in conjuction with 23rd International Workshop on Matrices and Statistics (IWMS) that took place in the second week. Conference Web Site: http://www.law05.si/law14/