We probably should be careful to say “eigenthings” in an effort to drive true understanding. It’s important to understand the difference between eigen values and eigen vectors, and not generalize them as eigen things. I’m not attempting to be pedantic. More so, I think it’s important to push the understanding of these esoteric “things.” I think Eric is generally correct though. Using eigen decomposition is useful because the result includes orthogonality. There are so many applications though, but two that stand out to be are PCA and Markov chains. @becausealice2 @erictleung. I’ll check out the forum. This discussion would be a great refresher on an important topic.