Question

7. (a) Show that if A is a real symmetric matrix such that $x_1$ and $x_2$ are eigenvectors with distinct eigenvalues $\lambda_1$ and $\lambda_2$, then $x_1$ and $x_2$ are orthogonal. (Hint: Show $\lambda_1 \langle x_1, x_2 \rangle = \lambda_2 \langle x_1, x_2 \rangle$. You may assume that symmetric matrices have real eigen- values.) (b) Explain how, using this information, you can compute an orthonormal eigenbasis for A. (In particular, be sure to address the case that A has a repeated eigenvalue.)

          7. (a) Show that if A is a real symmetric matrix such that $x_1$ and $x_2$ are eigenvectors
with distinct eigenvalues $\lambda_1$ and $\lambda_2$, then $x_1$ and $x_2$ are orthogonal. (Hint: Show
$\lambda_1 \langle x_1, x_2 \rangle = \lambda_2 \langle x_1, x_2 \rangle$. You may assume that symmetric matrices have real eigen-
values.)
(b) Explain how, using this information, you can compute an orthonormal eigenbasis
for A. (In particular, be sure to address the case that A has a repeated eigenvalue.)

7. (a) Show that if A is a real symmetric matrix such that x1 and x2 are eigenvectors
with distinct eigenvalues λ1 and λ2, then x1 and x2 are orthogonal. (Hint: Show
λ1 ⟨ x1, x2 ⟩ = λ2 ⟨ x1, x2 ⟩. You may assume that symmetric matrices have real eigen-
values.)
(b) Explain how, using this information, you can compute an orthonormal eigenbasis
for A. (In particular, be sure to address the case that A has a repeated eigenvalue.)

Added by Antonio S.

Question

Please give Ace some feedback