Tag Archives: basis vectors

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.

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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)\

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