how does operator overloading work in this code
<p>i made a mistake on how i posted my code it kind of showed that im lazy and i just want everything to be done for me,i want to learn about operator overloading in the code below and what this code is doing in the main program</p>

<pre><code>static public explicit operator Int32(Vector v)
        {
            return v.Length;
        }

        public override string ToString()
        {
            String res = "&lt;";
            for (int i = 0; i &lt; elements.Length; i++)
                res += " " + elements[i];
            res += " &gt;";
            return res;
        }

        public override bool Equals(Object v)
        {
            return (this == (Vector)v);
        }

        public override int GetHashCode()
        {
            return base.GetHashCode();
        }
    }
</code></pre>

<p>the code implements a class of vectors, by overriding the operations of addition, subtraction, multiplication of vectors and operators of equality / inequality. Take into account the operation where one operand - real or integer. Throw an exception in the case of coincidence of dimension vectors in operations.</p>

<pre><code>namespace ConsoleApplication3
{



    public class Vector
    {
        private Double[] elements;

        public Vector()
        {
            this.elements = null;
        }

        public Vector(Int32 size)
        {
            if (size &lt; 0) throw new Exception("Invalid vetors size");        
            elements = new Double[size];
        }

        public Vector(params Double[] elements)
        {
            this.elements = elements;
        }

        public Vector(Vector v)
        {
            this.elements = v.elements;
        }

        public int Length
        {
            get
            {
                if (elements == null) return 0;
                return elements.Length;
            }
        }

        public Double this[int index]
        {
            get 
            {
                return elements[index];
            }
            set 
            {
                elements[index] = value;
            }
        }

        static public Vector operator+(Vector v1, Vector v2)
        {
            if (v1.Length != v2.Length)
                throw new Exception("size of vectors are different");
            Vector res = new Vector(v1.Length);
            for (int i = 0; i &lt; res.Length; i++)
                res[i] = v1[i] + v2[i];
            return res;
        }

        static public Vector operator+(Vector v, Double d)
        {
            Vector res = new Vector(v.Length);
            for (int i = 0; i &lt; v.Length; i++ )
                res[i] = v[i] + d;
            return res;
        }

        static public Vector operator +(Double d, Vector v)
        {
            return (v + d);
        }

        static public Vector operator -(Vector v, Double d)
        {
            Vector res = new Vector(v.Length);
            for (int i = 0; i &lt; v.Length; i++)
                res[i] = v[i] - d;
            return res;
        }

        static public Vector operator -(Double d, Vector v)
        {
            Vector res = new Vector(v.Length);
            for (int i = 0; i &lt; v.Length; i++)
                res[i] = d - v[i];
            return res;
        }

        static public Vector operator *(Vector v, Double d)
        {
            Vector res = new Vector(v.Length);
            for (int i = 0; i &lt; v.Length; i++)
                res[i] = v[i] * d;
            return res;
        }

        static public Vector operator *(Double d, Vector v)
        {
            return (v * d);
        }

        static public Vector operator -(Vector v1, Vector v2)
        {
            if (v1.Length != v2.Length)
                throw new Exception("size of vectors are different");
            Vector res = new Vector(v1.Length);
            for (int i = 0; i &lt; res.Length; i++)
                res[i] = v1[i] - v2[i];
            return res;
        }

        static public Vector operator *(Vector v1, Vector v2)
        {
            if (v1.Length != v2.Length)
                throw new Exception("size of vectors are different");
            Vector res = new Vector(v1.Length);
            for (int i = 0; i &lt; res.Length; i++)
                res[i] = v1[i] * v2[i];
            return res;
        }

        static public Boolean operator ==(Vector v1, Vector v2)
        {
            if (v1.Length != v2.Length)
                return false;            
            for (int i = 0; i &lt; v1.Length; i++)
                if(v1[i] != v2[i]) return false;
            return true;
        }

        static public Boolean operator !=(Vector v1, Vector v2)
        {
            return (!(v1 == v2));
        }

        static public explicit operator Int32(Vector v)
        {
            return v.Length;
        }

        public override string ToString()
        {
            String res = "&lt;";
            for (int i = 0; i &lt; elements.Length; i++)
                res += " " + elements[i];
            res += " &gt;";
            return res;
        }

        public override bool Equals(Object v)
        {
            return (this == (Vector)v);
        }

        public override int GetHashCode()
        {
            return base.GetHashCode();
        }
    }

    class Program
    {
        static void Main(string[] args)
        {
            Vector v1 = new Vector(new Double[]{1, 2, 3, 4});
            Vector v2 = new Vector(2, 3, 4, 5);
            Console.WriteLine(v1 + " + " + v2 + " = " + (v1 + v2));
            Console.WriteLine(v1 + " - " + v2 + " = " + (v1 - v2));
            Console.WriteLine(v1 + " * " + v2 + " = " + (v1 * v2));
            Console.WriteLine(v1 + " * " + 7 + " = " + (v1 * 7));
            Console.ReadKey(true);
        }
    }
}
</code></pre>
