#EIGENVECTORS MATHEMATICA CODE#

PCA tries to compress as much information as possible in the first PC, the rest in the second, and so on….Derive the new axes by re-orientation of data points according to the principal components.Sort the eigenvectors by decreasing eigenvalues and choose k eigenvectors with the largest eigenvalues, these becoming the principal components.Compute eigenvectors and the corresponding eigenvalues.Scale the data by subtracting the mean and dividing by std.So lastly, we have computed principal components and projected the data points in accordance with the new axes. In the last step, we need to transform our samples onto the new subspace by re-orienting data from the original axes to the ones that are now represented by the principal components.įinal Data= Feature-Vector*Transpose(Scaled(Data)) Recasting data along Principal Components’ axes I wrote a version of this for the Wolfram Demonstrations Project.After choosing a few principal components, the new matrix of vectors is created and is called a feature vector. 0 is always represented by black and 1 by white this makes it easy to identify 0’s and 1’s and do investigations about concepts like units, zero-divisors, nilpotents, and so on. This notebook has a manipulation which lets you visualize operations in modular arithmetic (such as addition or multiplication modulo n) by assigning a color to each number and then creating the operation table. The table can also be used to computer orders of elements, centralizers, etc.ĭownload this or other Higher Algebra notebooks from Google Drive Modular Arithmetic Once you have the Cayley table you can easily see that this is a group of 6 elements, and since the table isn’t symmetric about the main diagonal the group is non-Abelian, and therefore must be isomorphic to S_3. The example below shows a quick construction of the Cayley table for the group GL(2,Z_2). Both allow for the use of arbitrarily labels for the elements, and the MakeRingTables command requires you to put in labels for each of the tables so you can tell which is which. The commands CayleyTable and MakeRingTables allow you do to tables for either one or two operations respectively. This notebook contains codes to let you quickly create “Cayley Tables” – operation tables that are commonly used to understand small groups and rings.

#EIGENVECTORS MATHEMATICA CODE#

Solving a linear system is a great example of both being able to understand and algorithm and then code it.ĭownload this or other Higher Algebra notebooks from Google Drive Cayley Tables The code works by first checking if a system is linear in given variables, then putting the system in matrix form, performing Gauss-Jordan elimination on the resulting matrix, and then converting the reduced matrix to standard Mathematica notation. This notebook contains some code we wrote in our Technology 2 class to solve systems of linear equations (essentially duplicating a very small part of the functionality of Mathematica’s Solve command). You can also choose to have the true eigenvectors or eigenvalues displayed for reference.ĭownload this or other Higher Algebra notebooks from Google Drive A “home-brewed” solver for systems of linear equations Of course you will only be able to do this if the eigenvalues for the linear transformation are real. Your vector will be an eigenvector if the result vector is a scalar multiple of it – that is, if it is in the same or opposite direction. You can then drag around the terminal point of a vector (in red) and the computer will plot the image of your vector under the transformation in green. In this case you can enter in a linear transformation in x and y. This notebook gives a graphical demonstration of what it means to be an eigenvector. Important Note: The links for the notebooks open a new window or tab with a Google Drive page – the current settings for our homepages won’t allow me to host mathematica notebooks locally. Mathematica Notebooks for Linear & Abstract Algebra Financial Aid & Costs Toggle Toggle Close.

Eigenvectors mathematica