Tags » Eigenvalues

Principal Component Analysis Tutorial

Recently I have been reading up on Principal Component Analysis (PCA).  PCA is essentially a compression technique, providing a means of representing larger or high dimensional data sets with less information.   1,592 more words


Solution to the Clebsch puzzle

Here is the solution to the puzzle about the Clebsch graph I posed at the weekend. Since Gordon and Tony (and probably others) have already solved it, I am giving you my solution now. 459 more words

Principal Component Analysis Explained Visually


“Principal component analysis (PCA) is a technique used to emphasize variation and bring out strong patterns in a dataset. It’s often used to make data easy to explore and visualize.”

Applets / Interactives

Linear Algebra II: Eigenvectors and Diagonalisability

This post continues the discussion of the Oxford first-year course Linear Algebra II. We’ve moved on from determinants, and are now considering eigenvalues and eigenvectors of matrices and linear maps. 1,436 more words


Symmetric Matrices and Positive Definiteness

Symmetric matrices have three important properties that make it the ‘ideal’ matrix to have:

1.) Symmetric matrices satisfy 

2.) For a symmetric matrix with real entries, the eigenvalues are also real… 531 more words


Differential equations and exp(At)

How would you solve the following system of linear first order differential equations?

We can write this in matrix form:

Where and . Our first step is to write our system of differential equations in the form . 504 more words


'Diagonalisation' and the Fibonacci Sequence

We now know what eigenvalues and eigenvectors are and how to compute them but now what can we do with them? We will quickly see that the eigenvalues and eigenvectors offer a greater glimpse on the properties of matrix . 499 more words