Let B be a 4times4 positive-definite real symmetric matrix which is not the identity matrix. Consider the inner product on R^4 given by langle v,wrangle=v^topBw, where v^top denotes the transpose of v. Which of the following statements is FALSE?

(B) If v is an eigenvector of B and wneq0 is such that langle w,vrangle=0, then w is an eigenvector of B.

Q31Section B (Part B)31 of 120

Inner product spaces — which property of a weighted inner product fails

Let $B$ be a $4\times4$ positive-definite real symmetric matrix which is not the identity matrix. Consider the inner product on $\mathbb{R}^4$ given by $\langle v,w\rangle=v^{\top}Bw$ , where $v^{\top}$ denotes the transpose of $v$ . Which of the following statements is FALSE?

Pick an option to check your answer.

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