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Earlier quoted context omitted.
> is the extra layer of indirection in any discipline when things are named after people and not the thing’s characteristics. "Eigen" in German has same English root as "own": "Eigenvalue" is Germanglish for "Own/inherent value", so meets your spec of naming a thing after its characteristics, as long as "naming" is allowed to be in multiple languages.
It doesn't mean "same". It means "own" in the sense of "inherent" or "characteristic".
Does anyone know of an example of a simple physical system where eigenvalues have a physical interpretation? The examples I know of are all in quantum mechanics, which is a bit abstract for me.
Who is this explainer aimed at? If you can understand the first sentence, you probably already know what an eigenvalue is.
I was blown away in my Digital Signal Processing (DSP) class that eigen "values" exist for certain systems in the form of "waves". Basicaly you put in a wave made from multiple sine and/or cosine waves through some function f(x) and the output is STILL a wave, though its frequency, amplitude and phase might change. Technicaly if I remember correctly this applies to all complex exponentials, since those can be rewritt…
Earlier quoted context omitted.
If you learn a lot of math, a lot of names will hint at what they are so you have less to memorize. :-)
Except when some smart jerk discovered like eight different things!
https://en.wikipedia.org/wiki/List_of_things_named_after_Leo...
I was blown away in my Digital Signal Processing (DSP) class that eigen "values" exist for certain systems in the form of "waves". Basicaly you put in a wave made from multiple sine and/or cosine waves through some function f(x) and the output is STILL a wave, though its frequency, amplitude and phase might change. Technicaly if I remember correctly this applies to all complex exponentials, since those can be rewritt…
Earlier quoted context omitted.
If you learn a lot of math, a lot of names will hint at what they are so you have less to memorize. :-)
Except when some smart jerk discovered like eight different things!
Earlier quoted context omitted.
I read an interview with Australian wire music composer Alan Lamb that a stringed instrument with multiple overtones vibrating on the string can be analyzed by breaking down the vibration into eigenvalues, but I've never found any reference material that explain that. I'm wondering if he was referring to FFT.
Complex exponentials are the eigenfunctions of the Fourier transform. In other words, frequency component values are the eigenvalues. https://en.m.wikipedia.org/wiki/Eigenfunction#Vibrating_stri...
Something that frustrates me, and maybe I’m just confessing my stupidity, is the extra layer of indirection in any discipline when things are named after people and not the thing’s characteristics. My doctor once told me “if you learn enough Latin, a lot of names in medicine will hint at what they are, so you have less to memorize.” I find that these names often lend a sense of complexity to concepts that turn out to…
If such a word doesn't exist, you might as well name it after a person instead of trying to invent a new word.