Matrix Multiplication
A Matrix can be multiplied
- by a scalar
- by a vector: Matrix-Vector Multiplication
- by another matrix Matrix-Matrix Multiplication
Scalar Multiplication
To multiply a matrix on scalar, multiply each element $a_{ij}$ of the matrix on this scalar:
$A = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n}\ a_{21} & a_{22} & \cdots & a_{2n}\ \vdots & \vdots & \ddots & \vdots \ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix}$, then $c \cdot A \begin{bmatrix} c \cdot a_{11} & c \cdot a_{12} & \cdots & c \cdot a_{1n}\ c \cdot a_{21} & c \cdot a_{22} & \cdots & c \cdot a_{2n}\ \vdots & \vdots & \ddots & \vdots \ c \cdot a_{m1} & c \cdot a_{m2} & \cdots & c \cdot a_{mn} \end{bmatrix}$