Cartan–Dieudonné theorem
So imagine you have a big puzzle with many different pieces. Some of the pieces are easy to move around and rotate, but others are more stubborn and don't want to budge.
The Cartan-Dieudonné Theorem is a way of understanding how some of these puzzle pieces can be moved and rotated with the other pieces.
Basically, it says that any linear transformation (which is a fancy way of saying a way of changing the shape of something) can be broken down into a series of simpler transformations that involve only rotating certain pieces of the puzzle.
This is really helpful because it lets us understand how some complicated things can be broken down into simpler parts, sort of like taking apart a big machine and understanding how each small piece works by itself.
Overall, the Cartan-Dieudonné Theorem helps us understand how to apply mathematical concepts to complex problems by breaking them down into simpler parts.
The Cartan-Dieudonné Theorem is a way of understanding how some of these puzzle pieces can be moved and rotated with the other pieces.
Basically, it says that any linear transformation (which is a fancy way of saying a way of changing the shape of something) can be broken down into a series of simpler transformations that involve only rotating certain pieces of the puzzle.
This is really helpful because it lets us understand how some complicated things can be broken down into simpler parts, sort of like taking apart a big machine and understanding how each small piece works by itself.
Overall, the Cartan-Dieudonné Theorem helps us understand how to apply mathematical concepts to complex problems by breaking them down into simpler parts.