template class error

gistfile1.txt

// declaration
template<typename T>
friend std::ostream& operator<<(std::ostream& os, const LiteMatrix<T>& rhs); // works

template<typename T>
friend std::ostream& operator<<(std::ostream& os, const LiteMatrix& rhs); // compiler error
// cannot access private member declared in class

friend std::ostream& operator<<(std::ostream& os, const LiteMatrix& rhs); // linker error

friend std::ostream& operator<<(std::ostream& os, const LiteMatrix<T>& rhs); // linker error

// implementation
template<typename T>
std::ostream& operator<<(std::ostream& os, const LiteMatrix<T>& rhs)
{
	for (size_t i = 0; i < rhs.m_rows; ++i)
	{
		for (size_t j = 0; j < rhs.m_cols; ++j)
			os << std::setw(6) << std::fixed << std::setprecision(2) << rhs.m_mat[i * rhs.m_cols + j] << ' ';

		os << '\n';
	}
	return os;
}

//////////////////////////////////////////////////////////////////////////////////////////////////////////////

// other option is all in the class declaration
// this works
friend std::ostream& operator<<(std::ostream& os, const LiteMatrix& rhs)
	{
		for (size_t i = 0; i < rhs.m_rows; ++i)
		{
			for (size_t j = 0; j < rhs.m_cols; ++j)
				os << std::setw(6) << std::fixed << std::setprecision(2) << rhs.m_mat[i * rhs.m_cols + j] << ' ';

			os << '\n';
		}
		return os;
	}