題組內容

5 Let \( \mathbf{x},\mathbf{y}\in \mathbb{R}^n \) and \( A = I_{n} - \mathbf{x}\mathbf{y}^{T} \)

d. (8) Let \( \mathbf{x} \) and \( \mathbf{y} \) be nonzero vectors. Show that if \( \mathbf{x}^T\mathbf{y} = 0 \) then \( A \) is not diagonalizable.