Quick Linear Algebra notation question

[jofree87]

For transformations, what exactly does T(x) mean?

Does it mean T is the transformation matrix multiplied by a vector?

How about T(x₁, x₂) ?

 

[ystael]

$$T(x)$$ (or simply $$Tx$$) means the result of applying the transformation $$T$$ to the vector $$x$$. If you have the coordinate representations of these objects, i.e., the matrix of $$T$$ and the coordinates of the vector $$x$$, then the coordinates of the vector $$Tx$$ are indeed given by multiplying the matrix of $$T$$ by the coordinate vector of $$x$$, in that order.

If $$T$$ happens to be a transformation whose domain space is two-dimensional, then $$T(x_1, x_2)$$ probably means the result of applying $$T$$ to the vector $$(x_1, x_2)$$ where $$x_1, x_2$$ are numbers. If the domain space of $$T$$ is other than two-dimensional, there is no obvious candidate for the meaning of $$T(x_1, x_2)$$.