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Output parameter sensitivity for linear dynamic systems is treated in an operator framework. Parameter sensitivity is derived for a general linear system defined as the sum of linear operators on the initial state and control input. The sensitivity-related properties of insensitivity, sensitivity controllability, parameter identification and identifiability, and optimal control design for both minimum sensitivity and improved identification are then dealt with in terms of the sensitivity operators and their adjoints. This theoretical foundation is applied to give fundamental descriptions of the parameter sensitivities in linear ordinary differential equation systems. The discussion focuses on linear time-invariant systems where a new algebraic representation of the parameter sensitivities is obtained.