Hermite–Hadamard inequality
Okay kiddo, let's talk about the Hermit-Hadamard Inequality! Basically, it's a rule that helps us understand how different numbers behave when we add them up.
Imagine you have a bunch of numbers, let's say 1, 2, 3, 4, and 5. If we add them all up, we get 15. But what if we take some of those numbers away? Let's say we just add up 1, 3, and 5. That would give us 9.
What the Hermit-Hadamard Inequality tells us is that if we take the sum of these selected numbers (in this case 1, 3, and 5) and square it, it will always be less than or equal to the sum of the squares of each number individually (in this case 1^2 + 3^2 + 5^2).
This might seem like a bit of a mouthful but it basically means that even if we take away some numbers from the original list, we can always guarantee that the sum of their squares will be bigger than or the same as the squared sum of the numbers we selected.
So even if we remove some numbers, we can still figure out how big the answer will be when we add them up, just by looking at the size of the squares of each individual number.
Does that help, kiddo?
Imagine you have a bunch of numbers, let's say 1, 2, 3, 4, and 5. If we add them all up, we get 15. But what if we take some of those numbers away? Let's say we just add up 1, 3, and 5. That would give us 9.
What the Hermit-Hadamard Inequality tells us is that if we take the sum of these selected numbers (in this case 1, 3, and 5) and square it, it will always be less than or equal to the sum of the squares of each number individually (in this case 1^2 + 3^2 + 5^2).
This might seem like a bit of a mouthful but it basically means that even if we take away some numbers from the original list, we can always guarantee that the sum of their squares will be bigger than or the same as the squared sum of the numbers we selected.
So even if we remove some numbers, we can still figure out how big the answer will be when we add them up, just by looking at the size of the squares of each individual number.
Does that help, kiddo?