I am trying to understand inverse matrixes more in depth.
I took the simplest example: 2 points in a 2d space and put it into a matrix.
$$\begin{pmatrix}5&7\\-2&3\end{pmatrix}$$
Calculating the inverse, we would get another matrix and another 2 points.
Where could this inverse be used / and for what purposes?
Can someone provide me with a trivial example (preferably in 2d)?
Best Answer
A $2\times 2$ matrix corresponds to a map of the plane to itself. Not surprisingly, the inverse matrix of that matrix corresponds to the inverse map.
For instance, the matrix $$ \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \phantom-\cos \theta \\ \end{bmatrix} $$ corresponds to a rotation of angle $\theta$ around the origin. The inverse matrix is $$ \begin{bmatrix} \phantom-\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \\ \end{bmatrix} $$ and corresponds to a rotation of angle $-\theta$ around the origin.