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Comment by antiform | Hacker News Reader

In linear algebra, for a given linear transformation (a certain kind of matrix which generally represents some operation) M, an eigenvalue of M is a scalar c such that given a non-zero vector v (called the eigenvector), Mv = cv, where multiplication on the left is matrix multiplication and multiplication on the right is multiplication of v by the scalar c.

The definition is significant because it says that for a certain vector v, the transformation M, no matter how complicated it may be, just scales v by a factor of c. This is useful, for instance, if you want to determine an axis by which to evaluate the range of the transformation, because by choosing an eigenvector, you are choosing a "simple" or "natural" perspective from which to evaluate the range.

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Look, I am good at Math. I even love Number Theory. But what you wrote scares me. Can I run away now?

(I hope to one day be able to look at it and say 'my, that is so simple...' like I do with high school math)

This is the problem I had with Linear Algebra. The first half of the class felt like I was just being drilled definitions. But once all the definitions click, it's rather simple.

Honestly Linear Algebra is the next time you have to do a 'jump' in the regular sequence of math.

You hit algebra, new concepts, you have to jump a little. Same with calculus. Linear algebra is that next time.

And it gets easier. Linear Algebra is no more complicated than calculus --- rather less so. But it tends to be more abstract.

The best thing about my linear algebra class was that the professor warned us about this up front. Yet, I still was not prepared for the onslaught of new words, and the bad part of the class is they were all defined in terms of more mathematical words, not concepts like this rubber band example.

Why do you think you're good at math, when confronted with evidence to the contrary? :)

Is there something specific about the parent post that you don't understand that I can try to explain?

That was the point of the "What are eigen values?" article. It was to give the intuition behind the scary mathematical definition.

I find this helpful, as it answers the all important questions 1) Why should I care? and 2) What is the basic problem that the scary math is trying to solve?

With answers to those questions in hand, you can return to the scary math and work out how it maps to those answers.

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