Centering matrix
Imagine you have a group of numbers, like 1, 4, 7, and 10. Now imagine you want to do some math with these numbers, but they're not centered around anything. That means there isn't one number they're all close to, and they're kind of scattered all over the place.
To fix this, you can make a new group of numbers that are all centered around something. This new group is called a centering matrix. Here's how you make it:
1. First, you find the average of all the numbers in your original group. This means you add them all up and then divide by how many numbers there are. In this case, you would add 1 + 4 + 7 + 10 and then divide by 4, which is the number of numbers. The average is 5.5.
2. Next, you make a new group of numbers that are all the same size as the original group. In this case, that means you make a group with 4 numbers.
3. Then, for each number in the new group, you subtract the average from the original group. So for the first number, you take 1 - 5.5, which is -4.5. For the second number, you take 4 - 5.5, which is -1.5. And so on.
4. Finally, you put all these new numbers into a matrix. A matrix is just a fancy word for a grid of numbers. So if you put these numbers into a matrix, it would look like this:
|-4.5 -1.5 1.5 4.5|
And that's it! Now you have a centering matrix that you can use to do some math. All the numbers are centered around the average of the original group, which makes it easier to work with them.
To fix this, you can make a new group of numbers that are all centered around something. This new group is called a centering matrix. Here's how you make it:
1. First, you find the average of all the numbers in your original group. This means you add them all up and then divide by how many numbers there are. In this case, you would add 1 + 4 + 7 + 10 and then divide by 4, which is the number of numbers. The average is 5.5.
2. Next, you make a new group of numbers that are all the same size as the original group. In this case, that means you make a group with 4 numbers.
3. Then, for each number in the new group, you subtract the average from the original group. So for the first number, you take 1 - 5.5, which is -4.5. For the second number, you take 4 - 5.5, which is -1.5. And so on.
4. Finally, you put all these new numbers into a matrix. A matrix is just a fancy word for a grid of numbers. So if you put these numbers into a matrix, it would look like this:
|-4.5 -1.5 1.5 4.5|
And that's it! Now you have a centering matrix that you can use to do some math. All the numbers are centered around the average of the original group, which makes it easier to work with them.