How do mathematicians pronounce "Hessian"?
From searching online I've learned that the term is named after Otto Hesse, a German, and that the German state of Hesse has lent its name to a boot. From online dictionaries I've learned that I should say "HESH - in" if I want to refer to the boot.
What if I want to refer to the matrix? How do mathematicians typically pronounce "Hessian"? This is a slightly different question than how to correctly pronounce Otto Hesse's last name.
On
I have always heard and pronounced Hesh-in (here in the United States). As you pointed out, I am unsure if this is actually correct!
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Otto Hesse's last name is the same German word as Hesse, the German state, and the fabric. It's pronounced "hesh-uhn". Because "-ian" is added it's an English word with no German equivalent.
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"Hessian" is also a well-known term in history because the princes of Hesse rented out their army to serve in various wars, notably the American revolution. Yes, it's pronounced "Hesh'n", just like Russian and Prussian, but unlike Cardassian or Circassian or the Vancouver Canucks hockey player Zack Kassian.
"HESH-in" is correct with respect to the matrix groups. The name itself is "HESS", pronounced like an "s" with the "e" silent.