C ++矩阵类 - 建议

我试图在C ++中构建一个模板化的Matrix类。下面是它的实现。
我实现了两个运算符+，+ =现在只是为了给出一个关于它的外观的想法，我认为最好是在继续进一步之前请求反馈。

I am trying to build a templated Matrix class in C++. Below is its implementation. I implemented two operators +,+= as of now just to give an idea on how it will look and I thought it would be best to ask for feedback before I proceed any further.

整个实现是公共的，也没有明确的绑定/错误检查，这是因为它不意味着一个完整的矩阵库，因此避免了不必要的代码。

The whole implementation is public and also there are no explicit bound/error checks, this is because its not meant to be a full fledged matrix library and hence avoided unnecessary code.

如果有人对此发表评论，将会非常有帮助，并且可能会建议一些改进或建议。

It would be very helpful if someone could comment on it and may be suggest a few improvements or suggestions.

谢谢。

Thank you.

template<class T>
class Matrix
{
    public:
    int r,c;
    vector< vector< T > >mat;

    Matrix() {}

    // Constructor to set the size of the matrix
    Matrix(int _r,int _c)
    {
        r=_r;c=_c;
        mat.resize(r);
        for(int i=0;i<r;i++)
            mat[i].resize(c);
    }
    // Constructor to build a matrix from a C 2d array
    // Pointer to the first element is passed (&arr[0][0])
    Matrix(T *arr,int _r,int _c)
    {
        r=_r;c=_c;
        mat.resize(r);
        for(int i=0;i<r;i++)
            for(int j=0;j<c;j++)
                mat[i].push_back(arr[i*c+j]);
    }
    template<typename U>
    Matrix<T>& operator +=(const Matrix<U>&M)
    {
        for(int i=0;i<r;i++)
            for(int j=0;j<c;j++)
                mat[i][j]+=static_cast<T>(M.mat[i][j]);
        return *this;
    }
    template<typename U>
    Matrix<T> operator +(const Matrix<U>&M)
    {
        Matrix<T>tmp=*this;
        return tmp+=M;
    }
};

template<typename T>
istream& operator >>(istream &in,Matrix<T>&M)
{
    in>>M.r>>M.c;
    Matrix<T>tmp(M.r,M.c);
    for(int i=0;i<M.r;i++)
        for(int j=0;j<M.c;j++)
            in>>tmp.mat[i][j];
    M=tmp;
    return in;
}
template<typename T>
ostream& operator <<(ostream &out,Matrix<T>M)
{
    for(int i=0;i<M.r;i++)
    {
        for(int j=0;j<M.c;j++)
            cout<<M.mat[i][j]<<" ";
        cout<<endl;
    }
    return out;
}

编辑：
谢谢大家的建议。

Thank you all for the suggestions.

我只有一个小问题，说我想实现错误检查（例如：检查边界，有效的参数等），但我想要提供用户有一个选项，完全禁用错误检查，有没有什么好的方法来实现这个？
我需要的是像例子：`ios_base :: sync_with_stdio（0）;.
再次感谢。

I just have one small question, say I do want to implement error checking (ex: checking for bounds,valid arguments etc..) however I do want the provide user with an option to disable error checking completely, is there any good way to implement this ? What I need is something like example:`ios_base::sync_with_stdio(0);. Thanks again.