Matrix Representation of Vectors

1. Vectors are represented as \(N \times 1\) Column Matrices or as Transpose of \(1 \times N\) Row Matrices, where \(N\) is the Number of Vector Components. The following shows Vector \(V\) represented as a Column Matrix and a Row Matrix
   
   \(V=\begin{bmatrix}v_1\\v_2\\v_3\\v_4\\ \vdots \\v_n \end{bmatrix}=\begin{bmatrix}v_1 & v_2 & v_3& v_4 & \ldots & v_n\end{bmatrix}^T\)
2. Any Vector \(V\) having 3 Components can also be represented as a Skew Symmetric Matrix (denoted by \(V_\times\)) as follows
   
   \(V=\begin{bmatrix}v_1 \\ v_2 \\ v_3\end{bmatrix}\hspace{6mm}\Rightarrow V_\times=\begin{bmatrix}0 & -v_3 & v_2 \\v_3 & 0 & -v_1 \\-v_2 & v_1 & 0\end{bmatrix}\)
   
   The Skew Symmetric representation can be used to calculate Cross Product of Vectors in form of Matrix Multiplication