Is it true to say that every Finslerian manifold can be isometrically embedded in some $M\_{n}(\mathbb{R})$ with operator norm?


Note that every Riemannian manifold can be embedded in some matrix space isometrically, since the matrix space contains a copy of the standard $\mathbb{R}^{n}$:


[Hilbert-irreducible Banach space](https://mathoverflow.net/questions/253470/hilbert-irreducible-banach-space/253471#253471)



The Finslerian version of the Nash embedding theorem
[Burago and Ivanov](http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=aa&paperid=370&option_lang=eng) have shown that any compact Finsler manifold can be isometrically embedded into a finite-dimensional normed space. They also furnish examples of non-compact Finsler manifolds that can not be isometrically embedded in any finite-dimensional normed space. 


