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Two distinct Eigenvectors corresponding to the same Eigenvalue are always linearly dependent.

So i know this statement is false, but i don't understand the reason given by the book.

"" The vectors (1,0), (2,0) are both the eigenvectors of the matrix

\begin{pmatrix} 1 & 0 \\ 0 & 0 \\ \end{pmatrix}

corresponding to the same eignevalue 1.""

Aren't both vectors are linearly dependent?

  • 1
    No: $2(1,0)+(-1)(2,0)=(0,0)$.2012-12-15
  • 1
    What book is it?2012-12-15

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