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Let's Deduce Vandermonde Determinant in a More Natural Way

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Tags: linear-algebravandermonde-determinant

Vandermonde determinant is an elegant but weird result in the field of special determinant. Why do we need to calculate it? How do people discover it? And how do we get the result with our stunning attention (All things proven by mathematical induction are like this, so I have a natural aversion to mathematical induction.)? If you are a little more inquisitive, you may ask why the commonly used notation is x instead of other letters? I used to be fooled like this, but now with enough knowledge, a flash of inspiration has come to me, and I have finally found a natural way to prove it.

https://zhuanlan.zhihu.com/p/1925523222247473396

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5 Overall score*

54 Rank

7 Votes

4 Comments

Comments

This is a solid presentation of a standard result. I wouldn’t say it brings much to the table in terms of new insights or motivation, but it is clear and relatively easy to follow.

There is a small portion of mathematicians, who can actually understand a maths paper in full; most papers are too specific to be read by anyone outside the field, sadly this article while good falls into this category. Further more only results of calculation were given, you didn’t show your work, which undermined a beautiful connection. Relatively clear, but in practice vague to the reader. Maybe a bit harsh as the article spoke volumes, but I could not hear it.

7.7

Rediscovering the Vandermonde determinant by approaching the problem of polynomial interpolation from two different directions, setting the two solutions equal to each other, and moving some thing around. (Very neat! Would have appreciated some clarification on what Vandermonde matrices and Cramer’s rule are, though.)

8.5

It was great, if i couldnt find anything better then this will surely update it to 9 !