Theory

Multiply matrices

Two matrices can be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix. The process is called the dot product where the terms in each row of the first matrix are multiplied with the terms in each column of the second matrix.

⎣ ⎢ ⎡ a c e b d f ⎦ ⎥ ⎤ \cdot [χ_{1} χ_{2}] = ⎣ ⎢ ⎡ a \cdot χ_{1} + b \cdot χ_{2} c \cdot χ_{1} + d \cdot χ_{2} e \cdot χ_{1} + f \cdot χ_{2} ⎦ ⎥ ⎤

The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second one. For example, multiplying a

2 \times 2

with a

2 \times 2

the dimensions of the product will be

2 \times 2

as well.

[2541] \cdot [3732] = [2 \cdot 3 + 4 \cdot 7 5 \cdot 3 + 1 \cdot 7 2 \cdot 3 + 4 \cdot 2 5 \cdot 3 + 1 \cdot 2]