# Interacting with Graphs : Mouse-over and lambda-queuer

In the previous post, I described how I’d put together a basic system to drive data selection/exploration through a queue. While generating more graphs, it became evident that the code for mouseover interaction followed a specific pattern. More importantly, using Basis to plot stuff, mandated that I look at the inverse problem; namely, determining the original point from the point under the mouse pointer. In this case, it was pretty simple, since I’m only dealing with 2D points. Here’s a video of how it looks like. The example shows the exploration of a covariance matrix.

# Matrix Theory: Basis change and Similarity transformations

### Basis Change

Understand that there is nothing extremely special about the standard basis vectors [1,0] and [0,1]. All 2D vectors may be represented as linear combinations of these vectors. Thus, the vector [7,24] may be written as:

$\left( \begin{array}{cccc} 7 \\ 24 \end{array} \right)\ = 7. \left( \begin{array}{cccc} 1 \\ 0 \end{array} \right)\ + 24. \left( \begin{array}{cccc} 0 \\ 1 \end{array} \right)\$

# Matrix Theory: Linear transformations and Basis vectors

### Symmetric Matrices

A symmetric matrix looks like this:

$A= \left( \begin{array}{cccc} a & d & n & w \\ d & b & h & e \\ n & h & c & i \\ w & e & i & d \end{array} \right)\$

Notice how the values are reflected across the diagonal a-b-c-d; this holds true for any symmetric matrix.