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).