ELI5- Eigenvalues and Eigenvectors?
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Imagine you have a big, magical toy box with lots of different toys inside. Each toy has a special power or ability, like being able to jump really high or change colors. Now, let’s say you have a special toy in your box that can transform any other toy into a new toy with a different power.
This special toy is like an “operator” in math, and the toys it transforms are like “vectors”. When the operator transforms a vector, it can give it a new power or ability, just like the special toy in your toy box.
Now, let’s say that there are certain vectors that, when transformed by the operator, end up becoming multiples of themselves. These special vectors are called “eigenvectors”, and the multiples that they become are called “eigenvalues”.
Think of it like this: if you have a toy car that can transform into a toy plane, and you transform it using the special toy in your toy box, it might become a toy plane that is twice as big as the original car. In this case, the car is the eigenvector and the factor of two is the eigenvalue.
So, in math, eigenvectors and eigenvalues are special properties of operators and vectors that can help us understand how they behave and change. They’re like special toys and powers that can help us solve problems and do cool things!
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