Eigenvalues as Measures of Instability in Financial Markets
Students of mathematics (like me) may initially find great difficulty in understanding Vectors, Matrices, Eigenvectors and Eigenvalues. A good way to understand them is to visualize. So in the 3-Dimensional chart above is a chart with an example of what Principal Component Analysis looks like. (The math applies to any number of dimensions but since humans cannot visualize more than 3 dimensions we use this diagram.) So above we have a box with axes x,y,z, showing 3 Eigenvectors-Red, Blue and Green. You can see that they are orthogonal (at right angles) to each other, thus reducing the dimensions of the data space and producing a data space which captures the highest degree of variance, that is the essence of the data. Now, Eigenvectors only show the direction of the vector. They length of the vectors is the Eigenvalue.Eigenvalues tell you how much the data spreads out along each axis (how important each direction is). So, PCA helps you find the most meaningf...
