Matrix
| |
\[
\begin{aligned}
A &= \left[\begin{array}{rrrr}
a_{11} & a_{12} & \cdots & a_{1n}\\
a_{21} & a_{22} & \cdots & a_{2n}\\
\vdots \\
a_{m1} & a_{m2} & \cdots & a_{mn}\\
\end{array}\right] \\
\\
&= \left[\begin{array}{rrrr}
\vec{v_1} & \vec{v_2} & \cdots & \vec{v_n} \\
\end{array}\right]
\end{aligned}
\] |
Vector
| |
\[
\begin{aligned}
\vec{x} = \left[\begin{array}{r}
x_1 \\
x_2 \\
\vdots \\
x_n \\
\end{array}\right]
\end{aligned}
\] |
Product
| |
\[
\begin{aligned}
A \vec{x} &= \left[\begin{array}{rrrr}
x_1 \vec{v_1} + x_2 \vec{v_2} + \cdots + x_n \vec{v_n} \\
\end{array}\right] \\
&= \left[\begin{array}{rrrr}
x_1 \left[\begin{array}{r}
a_{11} \\
a_{21} \\
\vdots \\
a_{m1} \\
\end{array}\right] +
x_2 \left[\begin{array}{r}
a_{12} \\
a_{22} \\
\vdots \\
a_{m2} \\
\end{array}\right] +
\cdots +
x_n \left[\begin{array}{r}
a_{1n} \\
a_{2n} \\
\vdots \\
a_{mn} \\
\end{array}\right]
\\
\end{array}\right]
\end{aligned}
\] |
which is an m-dimensional vector.
# posted by rot13(Unafba Pune) @ 4:25 PM
