Reciprocity in linear system

Linear system

A linear system is a mathematical model of a system based on the use of a linear operator.Linear systems typically exhibit features and properties that are much simpler than the general, nonlinear case....

s is the principle that a response Rab, measured at a location (and direction if applicable) a, when the system has an excitation signal applied at a location (and direction if applicable) b, is exactly equal to Rba which is the response at location b, when that same excitation is applied at a. This applies for all frequencies of the excitation signal. If Hab is the transfer function

Transfer function

A transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant system. With optical imaging devices, for example, it is the Fourier transform of the point spread function i.e...

 between a and b then Hab = Hba, if the system is linear.

In the special case of a modal analysis

Modal analysis

Modal analysis is the study of the dynamic properties of structures under vibrational excitation.Modal analysis is the field of measuring and analysing the dynamic response of structures and or fluids when excited by an input...

 this is known as Maxwell's reciprocity theorem 

The reciprocity principle is also used in the analysis of structures. When combined with superposition

Superposition principle

In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...

, symmetry and anti-symmetry, it can be used to resolve complex load conditions.