Proof Routh-Hurwitz conditions at order 3

[abstract mason]

Do u have a document with this result ? I need it for a redaction of an appendix.
A polynomial : z^3+a_1 z^2+a_2 z+a_3 and his (complexs) solutions z-1,z_2 and z_3 (with multiplicities).
The assertion a_1,a_3>0 and a_1 a_2-a_3>0 <=> Re(z_1),Re(z_2)Re(z_3),<0
Tanks so much for ur informations, i found nothing until here.

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[pallid comet]

You want a proof only for n=3?

Why not just put a reference to routh Hurwitz in your appendix or do you need to show how ou derive your iff condition from routh Hurwitz directly?

[abstract mason]

Indeed that's enough

[pallid comet]

Hmm I see let me try

[abstract mason]

This appendix must be itself a justification of this result

[pallid comet]

I had a bit of an ink emergency and spilled a little when I was filling my pen but here you go i hope you can read it clearly

It is not exactly the same as yours a1, a3>0 and nonzero is the same but I got a1a2-a3>a1 not >0 as you have mentioned

Image is taking some time to upload 😔

[abstract mason]

i read perfectly with zoom

[abstract mason]

even it was so fast

i ll look what is a routh table and her properties

[pallid comet]

I used this as a reference

Contains proof and explaination

If you wish to have a paper instead of lecture notes

[abstract mason]

how do u get it ?

i think i see the secound, but i beilived it was too distant of my searches

Thanks so mush anyway, it ll be very usefull

[pallid comet]

Just googled proof of routh Hurwitz and checked a few different PDFs to find the clearest one

[pallid comet]

You're welcome good luck with the paper

[abstract mason]

i would switch my google to english for these researchs

[pallid comet]

Would help i reckon

I get very confused when i see French math sources too they teach you things slightly differently it seems

[abstract mason]

For what level for instance ?

Im not surprised by english ressources, even i check these who are more advanced than my lessons

[pallid comet]

Higher undergrad post grad mainly

Lot of modern math was done in France and written in French so getting sources for that is hard

Grothendieck and all for example

But that's very advanced for me you spot tiny oddities here and there tho with french curriculum i just can't remember a example now

[abstract mason]

hum okay