Dot Product of 2 Row/Column Matrices

1. Dot Product of 2 Column Matrices or 2 Row Matrices or a Row Matrix and a Column Matrix can be calculated Only if both the Matrices have the Same Number of Components/Elements.
2. The Dot Product is calculated by Multiplying the Corresponding Components of 2 Row/Column Matrices and Adding up All the Products. For example lets consider a Column Matrix \(A\) and a Row Matrix \(B\) each having \(N\) Components as given in the following
   
   \(A= \begin{bmatrix}a_1\\a_2\\ \vdots \\a_n \end{bmatrix}\hspace{.5cm} B= \begin{bmatrix}b_1&b_2& \cdots &b_n \end{bmatrix}\)
   
   The Dot Product of \(A\) and \(B\) is calculated as follows
   
   \(A \cdot B = B \cdot A = a_1b_1 + a_2b_2 + \cdots + a_nb_n\)