Assuming I have never taken linear algebra, just basic algebra…. What is an eigenvector? Plz explain like I’m 5
In: Mathematics
Imagine a really complicated series of train tracks that go every which way crossing a fault line where there are a lot of earthquakes. Just tons of tracks going all over the place.
One day there is an Earthquake and the ground shakes and all the train tracks move around.
Let’s agree every train track experiences the same Earthquake motion.
Almost all the train tracks get pulled and stretched and broken as the ground shifts.
One special track, though, was in just the right spot where the Earthquake *pulled it* along the direction it was pointed in anyway, so it just got a teeny bit longer. In a sense, its the only track that survived the Earthquake without changing shape, being bent, or breaking, but it’s length did change slightly.
What was special about that train track was both, the exact type of Earthquake that happened, and the direction the track happened to be in in the first place, those two qualities “paired up” to make a train track that didn’t bend or break, it just got **longer**. *That’s an Eigenvector*.
In math we often do things called “Linear Transformations” that are like my Earthquake, they take old lines and shift them into new lines. Some old lines though, are perfectly paired up to that specific transformation, that specific earthquake, and they won’t shift into a new direction afterwards, they’ll just be stretched or squashed down by it, and we call those the “Eigenvector” of that transformation.
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