Eigenvalues and Sorting

This week in Computer Science, we learned about sorting algorithms, and, recently, I learned about eigenvectors and eigenvalues in Linear Algebra, which do share some grounds for comparison.

Linear algebra often involves the multiplication of matrices and vectors, in which a matrix is essentially a grid of numbers and vectors are represented by a column of numbers. It is not a difficult operation, but it can be tedious. It leaves lots of room for simple errors in calculation and is wearisome for larger matrices. However, the concept of eigenvectors and eigenvalues reduces this time-consuming task into simple scalar multiplication, which is considerably easier.

One may ask: what's the point of sorting? Can't a collection of items be dealt with in an unordered manner? Does it really make a difference to have something sorted? Although sorting isn't always necessary, there are countless cases in which sorting makes complex tasks very simple. Imagine trying to find someone's number in an unordered phone book and you'll understand very quickly.

Yes, you can work with unordered collections just as you can work with matrices and vectors, but with powerful concepts like eigenvectors and sorting, why not take the shortcut where applicable? There is a large array of tools at our disposal as computer scientists, since we are able to use a variety of sorting techniques like insertion sort, quick sort, merge sort, and other sorting algorithms. The trade-off is worth it most of the time, being able to use a simple sorting function to make a collection's behaviour predictable and more manageable.

In the long run, sorting can make our solution to a problem more efficient and less time-consuming, just like eigenvectors in linear algebra. I hope to master and make use of these weapons at my disposal, and I hope you do, too.