How to replace variables in an expression?

Question

I have generated a matrix using Mathematica,

$\left( \begin{array}{ccc} \text{cos$\theta $} & -\text{sin$\theta $} & \text{cos$\theta $}\, \text{dx}+\text{dx}-\text{dy}\, \text{sin$\theta $} \\ \text{sin$\theta $} & \text{cos$\theta $} & \text{cos$\theta $} \,\text{dy}+\text{dy}+\text{dx}\, \text{sin$\theta $} \\ 0 & 0 & 1 \\ \end{array} \right)$

Now I want to change the variable names $dx$ to $xr$ and $dy$ to $yr$. How could I do this?

Answer 1

You can do it programmatically using Replace. For example:

{{1, 1, 1}, {1, dx, x^2}, {1, dy, du^2}} /. {dx -> s, dy -> "hello"}

replaces the dx with s and the dy with "hello". You can choose your own replacements. To understand what this actually means, consider the longer form:

Replace[{{1, 1, 1}, {1, dx, x^2}, {1, dy, du^2}}, {dx -> s, dy -> "hello"}, 2]

which shows that you want to replace the specified items in the second level (the "2") of the matrix.