LinkBuilder doesn't include Matrix Variables

If an endpoint uses Matrix Variables and you try to create a link to this method, the passed matrix variables aren't inserted into the link. The issue popped up in this Stack Overflow question.

See the following endpoint as an example:

@RequestMapping(value = "/matrix", method = RequestMethod.GET)
public HttpEntity example(
      @MatrixVariable String first,
      @MatrixVariable(required = false) String second) {
  return new HttpEntity<>("first=" + first + " second=" + second);
}

Using linkTo(methodOn(MvcController.class).example("First", "Second")).withSelfRel().getHref(); produces http://localhost:8090/matrix
whereas it should be http://localhost:8090/matrix;first=First;second=Second

As I outlined in the SO answer it is most likely that the UriBuilder implementation just doesn't consider matrix parameters:

1. See this part of the UriTemplate. It uses different variable types to build the Uri. A matrix parameter isn't one of them.
2. See the VariableType enum, which was used to do the switch on. There is also no matrix param.

There should be a possibility to create links with matrix variables.

Start with UriTemplate.java around the referenced UriBuilder logic and TemplateVariable.java around the VariableType enum. Trace how linkTo(methodOn(...).example("First", "Second")) builds its URI, then verify that the resulting href includes ;first=First;second=Second for the example endpoint.