Okay I'll bite. What's a "spectra"?
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Replying to @JadeMasterMath
You mean: what's a "spectrum"? There are several different things called a spectrum in math: Analysis: https://en.wikipedia.org/wiki/Spectrum_(functional_analysis) … Algebra: https://en.wikipedia.org/wiki/Spectrum_of_a_ring … Topology: https://en.wikipedia.org/wiki/Spectrum_(topology) … I will explain one for free.
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Replying to @johncarlosbaez @JadeMasterMath
Are they all morally the same thing or is the word just unfortunately overloaded?
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Yes, the spectrum of an operator is a special case of the spectrum of a commutative ring: at least under favorable circumstances, the spectrum of the operator is the spectrum of the commutative ring of operators generated by that operator!
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This, by the way, is something we owe to Gelfan'd -- and by no means the least nice thing, either.
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