- #1

- 677

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^{T}is a Gramian Matrix.

When I tried calculating the matrix G and its eigenvalues for cases when x = [x1 x2]' and [x1 x2 x3]'

by actually working out the algebra, it turned out (if I didn't do any mistakes) that the eigen values are all zeros except one which is equal to (x1

^{2}+x2

^{2}OR x1

^{2}+ x2

^{2}+ x3

^{2}) depending upon the case.

Is this a standard result for a Gramian Matrix to have a single non-zero eigenvalue? If, yes, is there a simpler proof?

Thank you.