Matrix-Vector Product

Last updated Feb 22, 2022 Edit Source

• Math linear

The product of a matrix $A$ and a vector $v$ can be written as:

$$ Ax = \begin{bmatrix} a_1 & a_2 & … & a_n \end{bmatrix} \begin{bmatrix} x_1 \\x_2 \\… \\x_n \end{bmatrix} = x_1a_1 + x_2a_2 + … + x_na_n $$

Here entries in the form $a_c$ are all vectors

1. $A(u+v) = Au + Av$
2. $A(cu) = cA(u)$