Classes with same name in different namespace

I am writing a library. Is it a bad idea to have two classes with same name but each of the classes are in different namespace?

Using name spaces:

//forward declaration
namespace sparse {
    class matrix;
}
namespace dense {
    class matrix;
}

namespace dense {
    typedef Index uint64_t;
    class matrix {
        public:
        sparse::matrix tosparse();
    };
}

namespace sparse {
    typedef Index uint32_t;
    class matrix {
        dense::matrix todense();
    };
}

Alternatively, I can use long names:

class sparse_matrix
...