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Fuzzywhale
Registered User regular

For my PhD research I have come up with a giant system of quadratic forms that I would like to solve.

I have absolutely no idea how to tackle this . So any help math people could provide would be wonderful!

Editing for more info:

So this is some tensor algebra; I am unraveling an indexed equation into all of its components. I have maybe 30 equations that are of the form

x_1x_2+x_3_x4+x_5x_6+x_7x_8+X_9X_10+X_11X_12+X_13_X14+X_15X_16+X_17X_18+X_19X_20+X_21X_22-X_23X_24=0

Does Mathematica/Matlab/Maple Have any magic that can handle this? Alternatively can anyone recommend a nice linear algebra book? Granted I've only sat through 2 linear algebra courses but this sort of thing never came up for me.

I have absolutely no idea how to tackle this . So any help math people could provide would be wonderful!

Editing for more info:

So this is some tensor algebra; I am unraveling an indexed equation into all of its components. I have maybe 30 equations that are of the form

x_1x_2+x_3_x4+x_5x_6+x_7x_8+X_9X_10+X_11X_12+X_13_X14+X_15X_16+X_17X_18+X_19X_20+X_21X_22-X_23X_24=0

Does Mathematica/Matlab/Maple Have any magic that can handle this? Alternatively can anyone recommend a nice linear algebra book? Granted I've only sat through 2 linear algebra courses but this sort of thing never came up for me.

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## Posts

A brief google search turned up this fine document from MIT. Which may not be helpful as it is mostly math jargon, but you must know some math if you PhD requires you to deal with quadratic forms. It seems to deal with solving matrices of quadratic forms so maybe it'll help? Either way you get a bump from my post. Good luck with your research.

lifeincognitoonYeah I'm going to hit up some department members on monday. This has been my "thing to do" for maybe 3 weeks and i've kept botching it. I'm pretty clueless

FuzzywhaleonIf you have 24 variables, you should be able to specify coefficients on all of them and then add everything together. If you don't have that many unique products, you can make the products into new variables (like a variable called X_1*X_2) and then solve again once you have constraints on the products.

CrystalMethodistonIsn't that only valid for linear equations, that is, something like y=aX_1+bX_2+......?

Edit: Duh I see what you mean. I will try some substitutions.

Fuzzywhaleon