This question pertains to Matrix Transformations. So to provide an example, if I have 3D coordinates where $X = -1$ to $1$, $y = -1$ to $1$, $z = -1$ to $1$. They are "normalized" in my mind. Can I use a Matrix to transform these coordinates into a space using "scaling", "rotation", and "translation"? I'm not sure if I'm being specific enough. So if more information is needed. Please feel free to ask. :) Thanks in advance for any responses.
Edit:
To elaborate more on my question; I'm going to tell you what "want" to do because I feel it's right.
What I want to do is take some arbitrary coordinates in 3-D, and transform them into another space that's also 3-D. I have the matrices for this transformation, but I'm not sure if I can just use it directly like that. (I.E. Just multiply these arbitrary coordinates by "my" Matrix and have the results I expects.
Adding more information, Say I have a matrix that is concatenated Scaling, Rotation, and Translation. Can I take this single matrix multiply it with "Any 3D Coordinates that are currently defined in any arbitrary space"? Or, must I take these coordinates, perform "some" operation on them, then use "my" matrix. I hope I make sense. Thanks in advance again.
Your set $C = \{(x,y,z) \in \mathbb{R}^3 : |x| \le 1, |y| \le 1, |z| \le 1\}$ is a cube, obviously. Using a matrix transformation, you can transform this cube into any given parallelipiped, arbitrarily oriented in space. The matrix transformation will do the necessary rotation, scaling, and shearing. Tell us if that's actually what you want to do, and then the details can be added.