Some managers, like project managers, are responsible for directing the work of other employees, but are not responsible for the administrative management of those individuals. They do not discipline the employee, promote/demote them, do salary adjustments, etc.
Some individuals have manager in their title, but don't actually manage anyone else. These individuals also are not line managers.
In a typical matrix management structure, the project manager gives work direction to the project team members regardless of what department or functional group they came from. The people who run those departments and groups, who manage all the individuals in them, are the line managers.
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