Desmos | Beautiful, Free Math. Interpreting Logs. Dot Product. Matrix factorizations and social network graph analysis. This is a lecture post for my students in the CUNY MS Data Analytics program. In this series of lectures I discuss mathematical concepts from different perspectives. The goal is to ask questions and challenge standard ways of thinking about what are generally considered basic concepts. Consequently these lectures will not always be as rigorous as they could be. The LU decomposition Matrix factorizations along with spectral theory are two areas of linear algebra that are heavily used in practice.
The concept behind the LU factorization is fairly simple. Kuttler introduces the multiplier procedure immediately, but I think it’s illustrative to develop some intuition first. Solving for the unknowns yields . Is composed of all ones, which reduces to Therefore and In R we don’t have to go through this mechanical process as the multiplier algorithm credited to Dolittle is already implemented for us.
The LU factorization is useful primarily for mechanical reasons. Exercises that solve the equation . . Visualizing systems of linear equations and linear transformations. This is a lecture post for my students in the CUNY MS Data Analytics program. In this series of lectures I discuss mathematical concepts from different perspectives. The goal is to ask questions and challenge standard ways of thinking about what are generally considered basic concepts. Consequently these lectures will not always be as rigorous as they could be.
Solution sets for systems of linear equations Let’s look first at a simple system of linear equations with a single solution. This system is from Example 1.10.1 of Kuttler. What is this system telling us? , which can be graphed using the R code below. What happens if only two of the three equations are defined? Let’s redraw our graph with only these two functions, along with the new solution set. As a bonus, I drew the original solution when we had three functions. Notice that we arrived at this solution set by using only two of the three equations. Solving this system leads to the same situation, where the variables are dependent. Dan Meyer: Math class needs a makeover. Maths: If someone tells you "There is nothing related to math in real life", how can you respond him/her?
Forgot Algebra. Life Tip: X percent of Y is equal to Y percent of X.