Assuming I have never taken linear algebra, just basic algebra…. What is an eigenvector? Plz explain like I’m 5
In: Mathematics
I hope this analogy/post is allowed… don’t tell this to a literal five year old.
When my manager/producer asked me this question, I said take a condom and a sharpie. Magnum size is easier to work with. Wash it. Draw one arrow from the base to the tip. Draw another arrow in a circle that goes around the shaft. Draw a third arrow that from the base that is sort of diagonal between the other two arrows. Now stretch the condom length wise, the first arrow will get longer but will not change the direction. Now stretch it horizontally, the second arrow will stretch but not change the direction. The third arrow will change the direction in both cases. The arrows that don’t change the direction are your eigenvectors (under a particular linear transform), the amount of increase in length are your eigenvalues. These come in pairs eigenvalue/eigenvector. the larger the eigenvalue the more important the eigenvector is. I guess it is more important to have a long (censored) than a thick one under this logic.
Latest Answers