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I don't think using emscripten to compile C++ to JS is really the answer. Rather I see the examples that emscripten and asm.js suggest for perf that means you can could write a JS library that gives you the perf you want.
I'm absolutely against having a Matrix library built into the browser. It won't fit most use cases. It will be slower than ones like glMatrix. It will end up being cruft in the browser with a maintenance burden that means people will have to spend time on it when they could be spending time on more useful features.