Which languages do Pascal users come from, and to which do they go?
Which languages do Pascal users come from, and to which do they go?
https://erikbern.com/2017/03/15/the-eigenvector-of-why-we-moved-from-language-x-to-language-y.html
https://erikbern.com/2017/03/15/the-eigenvector-of-why-we-moved-from-language-x-to-language-y.html
https://erikbern.com/2017/03/15/the-eigenvector-of-why-we-moved-from-language-x-to-language-y.html
https://erikbern.com/2017/03/15/the-eigenvector-of-why-we-moved-from-language-x-to-language-y.html
You have far too much time on your hands. Wow. Why??
ReplyDeletesteve hughes What makes you think I wrote the article?
ReplyDeleteLooks like an experiment to me from which a conclusion is formed based on coincidence. Without a viable proof, that's all that can be surmised.
ReplyDeleteThe first eigenvector as noted by the author is referred to as the dominant eigenvector. It has this name because it points in the direction of maximum scaling and rotation imposed by the matrix. Thus it is dominant among all the eigenvectors. In a similar way, it has an associated dominant eigenvalue.
So it comes as no surprise that the dominant eigenvector points in the direction of the center of the probability distribution, i.e. the direction of maximum density.
Finally, it is not true that if you interate a square matrix with any vector that the result will converge to the first (dominant) eigenvector. The zero vector immediately produces a stationary point and a real matrix may have a complex dominant eigenvector which is out of reach if you start iterating with a real vector.