TABLE OF CONTENTS If John gets 10 hectathrills by taking to a ball a lady aged 24 and of height 5 ft 5 ins, how many hectathrills would he obtain by taking to the same ball a lady of height 10 ft 10 ins and aged 48? (With apologies for the failure to use SI units and with acknowledgments to Linderholm, 1972.)
In the linear world, the relation between cause and effect is constant and the relation is quite independent of magnitude. For instance, if a force of 1 newton, applied to a mass m, causes the mass to accelerate at a rate a, then according to a linear model, a force of 100 newtons, applied to the same mass, will produce an acceleration of 100 a.
Strictly a linear function f must satisfy the following two conditions, where it is assumed that the function operates on inputs u 1( t), u 2 ( t), u 1 ( t) + u 2 ( t), ?u( t), where ? is a scalar multiplier:
f( u 1 ( t)) + f( u 2 ( t)) = f( u 1 ( t) + u 2( t))
f( ?u 1( t)) = ?f( U 1( t)).
Any system whose input-output characteristic does not satisfy the above conditions...
