Strong dual space

Imagine you have a toy chest full of toys. Each toy is special and has its own unique qualities. Now, imagine you have a special notebook where you can write down what each toy is like. Maybe you write down that your teddy bear is soft and cuddly, while your toy truck is big and sturdy.

The toys in the chest are like mathematical "vectors" and the notebook is like a "dual space".

Now, let's imagine you have a really strong friend who can lift all of the toys out of the chest at once! This is like a "linear functional" in math. Your friend is able to lift up all of the toys at once and tell you what each one is like without taking them out one by one.

The ability to lift up all of the toys at once and describe them is called the "strong dual space". It's like having a really strong friend who can do all the work for you! In math, the strong dual space is a way of describing the functionals that can lift up an entire set of vectors and describe them all at once.