The idea of this applet is to help to understand what Diagonalising a matrix achieves.[br]It is my first attempt at writing anything in Geogebra, so apologies for the glitches[br]A is a transformation, which you can edit by double clicking on it. [br]The applet will need reloading if A is a two way stretch along the x and y axes (i.e. if opposite entries are 0).[br]The normalised matrix of eigenvectors (P) and its inverse (Pinv) are calculated.[br]The Diagonalised matrix is also calculated.[br]Note that if you are working from the Edexcel syllabus, they only use symmetric matrices for A and the inverse of P will be its transpose.[br]The transformation P is applied to the co-ordinate system (the new grid shows the new Axes X' and Y' and a grid based on these axes at the same intervals as whatever the X,Y grid is showing; the X,Y grid is switched off but can be switched on by right clicking on the screen)[br]The transformation A can be considered as a stretch along the new X' axis and a stretch along the new Y' axis with scale factors given by the values in the Diagonalised matrix.[br]If you grab point L and drag it around, you will see its coordinates in the new system displayed as r'.[br]Pick L up, take it to an object point, and note down r'.[br]Now move it to the image, and note down the new r'.[br]You should see how the new x' and y' coordinates are simply the object x' and y' coordinates multiplied by the eigenvalues- showing the stretch clearly.[br]Enjoy; you can break it by using non-diagonalisable transformations or getting eigenvectors that are parallel to the x and y axes!