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Why linear algebra is called linear - you mean what is significance of the word linear in linear algebra?
Wiki User
∙ 13y ago
Linear algebra deals with mathematical transformations that are linear. By definition they must preserve scalar multiplication and additivity.
T(u+v)= T(u) + T(v)
T(R*u)=r*T(u) Where "r" is a scalar
For example. T(x)=m*x where m is a scalar is a linear transform. Because
T(u+v)=m(u+v) = mu + mv = T(u) + T(v)
T(r*u)=m(r*u)=r*mu=r*T(u)
A consequence of this is that the transformation must pass through the origin.
T(x)=mx+b is not linear because it doesn't pass through the origin. Notice at x=0, the transformation is equal to "b", when it should be 0 in order to pass through the origin. This can also be seen by studying the additivity of the transformation.
T(u+v)=m(u+v)+b = mu + mv +b which cannot be rearranged as T(u) + T(v) since we are missing a "b". If it was mu + mv + b + b it would work because it could be written as (mu+b) + (mv+b) which is T(u)+T(v). But it's not, so we are out of luck.
Wiki User
∙ 13y ago
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