Operations in the Field \mathbb{R^n}

As in any field, we can define the mathematical operations of the field \mathbb{R^n} .

These operations are:

• Addition
• Multiplication

We also need to define the zero and one element in the field.

• Zero element : \vec{x}=\begin{bmatrix} 0\\ 0\\ 0\\ :\\0\end{bmatrix}

• One element: \vec{x}=\begin{bmatrix} 1\\ 1\\ 1\\ :\\1\end{bmatrix}

The above operations satisfy the field axioms :

• Associativity
• Commutativity
• Distributivity
• Identity (defining zero addition and multiplication by one )
• Inverse (defining Subtraction-Additive Inverse and Division-Multiplicative Inverse )

In this lesson we will focus on** vector addition** and scalar by vector multiplication .