C/C++ :: Checking Typename In Templates

Suppose you have a templated class, such as

template <typename T>
class Matrix {
// some stuff and some methods
};

and let's say that you have some methods that need to do some type-dependent stuff, like, for example,

template <typename T>
Matrix<T> Matrix<T>::transpose() const {
// get this->rowCount, this->columnCount
// create a Matrix that has rowCount amount of columns and columnCount amount of rows
// copy (*this)[j][k] to theMatrix[k][j] (for all of the entries in *this)
// if the entries are complex, take the complex conjugate of them all
}

Would it be good practice to check explicitly for the typename parameter (or is this, somehow, defeating the purpose of templates)? std::cout << "I know that this is a design question, but it needs to be asked... ";