Abstract class method - To instantiate child class object?

Question

I'm trying to create a matrix library (educational purpose) and have reached an obstacle I'm not sure how to approach with grace. Adding two matrices is a simple task, using a method get() on each each matrices' elements individually.

However, the syntax I've used is wrong. NetBeans claims it's expecting a class, but found a type parameter; to me, a type parameter is just a set with 1:1 mapping to the set of classes.

Why am I wrong here? I've never seen a type parameter be anything else than a class before, so shouldn't the following bit imply M to be a class?

M extends Matrix

public abstract class Matrix<T extends Number, M extends Matrix>
{
    private int rows, cols;
    public Matrix(int rows, int cols)
    {
        this.rows = rows;
        this.cols = cols;
    }

    public M plus(Matrix other)
    {
        // Do some maths using get() on implicit and explicit arguments.
        // Store result in a new matrix of the same type as the implicit argument,
        // using set() on a new matrix.
        M result = new M(2, 2); /* Example */
    }

    public abstract T get(int row, int col);
    public abstract void set(int row, int col, T val);
}

Answer 1

You cannot instantiate a type parameter M directly because you don't know its exact type.

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I suggest thinking about creating the following method

public abstract <M extends Matrix> M plus(M other); 

and its implementation in the subclass.