Curious, something inherent in either transforming or adding either squares or exponents is causing a loss of information. I guess that something would be lost in transformation, not addition, so if information is lost in transformation then it would still be lost when they are then added together thus giving a different.
Thanks,ĮDIT: With a little inductive reasoning, it appears that if a translation is NOT linear, something is being lost or gained either when either the vectors are added together and then transformed, or something is lost or gained when they are transformed then added together. I hope I'm clear on the type of answer I'm looking for. I understand that it meets those three criterion, but say, in a very abstract sense (and hopefully in laymen's terms), what does it mean? Perhaps it implies continuity? Perhaps it means the transformation won't enter the domain of complex numbers?Īlso, can you name a condition or two where 'linearity', that is, the criterion will consistently broken? Simple question, (apologies if answered, I'm about 1/2 way through), but, what exactly does "Linear" mean.
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