Gram matrix

Imagine you have a bunch of friends and you want to know how much they are alike or different from each other. One way to do that is to compare all your friends with each other and see how much they share in common.

The gram matrix is like a chart that helps you do that comparison. You write down all your friends' names in one column and again in a row at the top of the chart. Then, for each friend, you compare them with every other friend and write down a number in the corresponding box.

This number represents how similar they are to each other. If two friends have a lot in common, the number will be high, while if they have little in common, the number will be low.

Once you have filled in all the boxes, the gram matrix will show you how similar or dissimilar your friends are to each other. You can use this information to group your friends based on their similarities, or to identify outliers who are very different from everyone else.

In the world of math, the gram matrix is used to represent the relationships between vectors in a high-dimensional space. But no matter what you're comparing, the gram matrix is a handy tool for understanding how things relate to each other.