Matrix Multiplication

Matrix multiplication is quite an extensive operation to do. When multiplying a matrix $A$ by another matrix $B$, each element from the result matrix $C$ is calculated by the rows of $A$ times the columns of $B$.

Before attempting, one should guarantee that the numbers of columns from $A$ is equal to the number of rows from $B$. The result $C$ will have the number of rows from $A$ and the columns from $B$.

$$\begin{array}{rl}& A_{m\times n}\ast B_{p\times q}=C_{m\times q}\\ & \text{given that }n=p.\end{array}$$

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Dot product

When multiplying matrices, one use the dot product, which is when matching members are multiplied, and then summed up. When working with matrices, a row is multiplied by a column, element-wise, and then summed up. For example:

    = 64$$ Doing this for every combination of $A$ *rows* and $B$ *columns*, we can build the entire $C$ result.