Consider a matrix . In general, this matrix has rank Now, suppose we wish to column-center the data. We can do this algebraically by using what is known as the centering matrix, where is the matrix where for all . Multiplying with results to the centering of all the columns. The vector of ones is the only independent element in its nullspace and so . … Continue reading Rank of centered data
In one of the previous posts, we talked about the Kaczmarz method for solving linear systems. This time, we are gonna provide three more ways to solve iteratively, namely via the methods of Gradient descent, Conjugate gradient and Newton’s method. We will also take a look at the codes, implementation was done for all of them in matlab. We will first look at how the methods are applied … Continue reading Searching for the minimum? Gradient descent to the rescue!
If you’ve thought of that too, then you should check this amazing video : It’s the best way to learn the answer and you’ll never forget it. Kudos to The Endeavour for sharing. Continue reading “I am still not quite sure … how can I tell that a matrix is invertible?”
I wanted to share with you a mathematical trick. Nothing too difficult, just not the first thing that someone would think. One of the important things in mathematics is to try to use the same tools for different jobs. Be creative! We will use the Caley – Hamilton theorem to calculate arbitrary powers of a matrix A. But first, let’s remember what the Caley – … Continue reading An idea for calculating powers of matrices