Matrix Notation For Vectors

A vector u = (u1, u2, …, un) can be written in column matrix form such that:

(1)
\begin{align} \vec{u} = \begin{bmatrix} u_1\\ u_2\\ ...\\ u_n \end{bmatrix} \end{align}

Or even row matrix form such that:

(2)
\begin{align} \vec{u} = \begin{bmatrix} u_1 & u_2 & ... & u_n \end{bmatrix} \end{align}

# Matrix Operations Analogous for Vector Operations.

Many of the operations that can be performed on vectors are analogous to than on matrices. For example, matrix substraction operates in the same manner such that:

(3)
\begin{align} \vec{u} + \vec{v} = \begin{bmatrix} u_1\\ u_2\\ ...\\ u_n \end{bmatrix} + \begin{bmatrix} v_1\\ v_2\\ ...\\ v_n \end{bmatrix} = \begin{bmatrix} u_1 + v_1\\ u_2 + v_2\\ ...\\ u_n + v_n \end{bmatrix} \end{align}