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coco richie
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Every definition I find on Google utilizes vector spaces and mapping which are mathematical. If you have to use vector spaces and mapping please explain the mathematics behind it. Thanks.
In fact, if f and g are linear, then f(g(x)) = g(f(x)), so we may as well write fg(x) = gf(x).
These two properties define a linear transformation, no matter how abstract the field of study is.
Just to be clear slider, are you referring to multiplication and addition as the two properties of the functions that define linear transformation? What other choices do we have that makes a function "non-linear"?
How would you word this equation? Is it f times g(x) is equal to g times f(x)?
Every definition I find on Google utilizes vector spaces and mapping which are mathematical. If you have to use vector spaces and mapping please explain the mathematics behind it. Thanks.
A translation is *not* a linear transformation; it is an affine transformation.
In fact, if f and g are linear, then f(g(x)) = g(f(x)), so we may as well write fg(x) = gf(x).
Possible interpretation: composition of linear functions is commutative. Counter example: rotations in R^{3}. So I guess it's not that... Could you disambiguate?