Relative gain array properties

What are the properties of a relative-gain array How many relative gains do you need to compute in order to specify completely the relative-gain array of a process with (a) three inputs and three outputs, and (b) N inputs and N outputs ... 

Controllability indices, as Closed Loop Disturbance Gain (CLDG) and Performance Relative Gain Array (PRGA) predict in all situations better dynamic properties for the forward heat-integration scheme, compared with the reverse one. This behaviour is verified by closed loop simulation with the full non-linear model. 

The relative gain array A has a property that makes the calculation of all the elements of the array unnecessary. This is shown in Equation W8.1 and apphed to a 2 x 2 system in Equation W8.2. A. refers to the relative gain between the ith controlled variable and Jth manipulated variable. 

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