I haven't used Tablematrix but here's some general information you may find useful.

See Tk::Widget (abstract base class for all Tk widgets) which has a lot of methods for querying metrics of this sort.

Tk::Wm (communicate with window manager) also has useful information.

I note you say "full screen" but don't show overrideredirect() (that's documented in Tk::Wm). The choice is yours but, if window decorations are displayed on the screen, you'll need to include their dimensions in your calculations. A note of caution: these dimensions will vary with operating system, window manager and user preferences.