Existance of solutions to set of quadratic equations

Leo321
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We have two unknown vectors x,y with real non negative values.
We can assume ||x||=||y||=1.
There are m known nxn matrices with real values.
We have m equations of the form:
yTA1x=0
...
yTAmx=0

What are the conditions for the existence of solutions for x,y?
What is the minimal number m and the condition on the matrices(linear independence, etc) for there to be no solutions?

Thanks
 
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