Monthly Archives: April 2020

This week, the main new computational topic is complex eigenvalues and eigenvectors. CoCalc finds complex eigenvalues / eigenvectors by default, so we already know how to find complex eigenvectors: A = matrix([[1,-2],[1,3]]) A.eigenvalues() A.eigenvectors_right() Note that CoCalc (Sage) uses “I” to stand for i, the square root of -1. (This choice is because “i” is often […]

Finding eigenvectors and eigenvalues is hard. Our general strategy was: Compute the characteristic polynomial. For an n x n matrix, this involves taking the determinant of an n x n matrix with entries polynomials, which is slow. (The fast method for computing determinants, row reduction, doesn’t help much since the entries are polynomials.) Find the roots […]

This post’s goal is to quickly get up to speed with doing linear algebra manipulations in Sage. Work through this, typing the code into Sage. Remember to press shift-return after each piece of code. Start by creating a new Sage worksheet. Pretty printing To make the matrices look nicer, type: %typeset_mode True and press shift-return. […]