Linear Algebra

These are my notes from working through Gilbert Strang’s Introduction to Linear Algebra.

Introduction to Vectors#

The core of linear algebra is vector addition and scalar multiplication. Combining these two operations gives us a set of linear combinations.

$
c\mathbf{v} + d\mathbf{w} =
c\begin{bmatrix}
1 \
2
\end{bmatrix} +
d\begin{bmatrix}
3 \
4
\end{bmatrix} =
\begin{bmatrix}
c + 3d \
2c + 4d
\end{bmatrix}.
$The vectors $c\mathbf{v}$ lie along a line. If vector $\mathbf{w}$ is not on that line, the set of linear combinations $c\mathbf{v} + d\mathbf{w}$ fill the entire two-dimensional plane, because there is a linear combination that reaches every point.