ML Wiki

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 $c \cdot A \begin{bmatrix} c \cdot a_{11} & c \cdot a_{12} & \cdots & c \cdot a_{1n}\\ c \cdot a_{21} & c \cdot a_{22} & \cdots & c \cdot a_{2n}\\ \vdots & \vdots & \ddots & \vdots \\ c \cdot a_{m1} & c \cdot a_{m2} & \cdots & c \cdot a_{mn} \end{bmatrix}$

Sources

• Linear Algebra MIT 18.06 (OCW)