Does the Matrix xyTA Have More Than One Non-Zero Eigenvalue?

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We have vectors x,y of size n and a matrix A of size nxn.
Is it true that the matrix xyTA has at most one non zero eigenvalue? Why is it so?
 
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Ok, I think I got it.
The matrix xyT has a rank of 1.
It is known that rank(AB)<=min(rank(A),rank(B))
Thus rank(xyTA)<=1
It is also known that the number of non-zero eigenvalues of a matrix is less or equal to the matrix rank. Thus the number of non-zero eigenvalues of xyTA is at most 1.
Right?
 
xy(transpose) will yield a scalar correct?

That means the maximum number of eigenvalues is n i believe
 
khemist said:
xy(transpose) will yield a scalar correct?


no, xTy is a scalar
 

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