15. Symmetric Matrices, Spectral Ideas, and Applications

Orthogonal Diagonalization — Quiz

Test your understanding of orthogonal diagonalization with 5 practice questions.

Practice Questions

Question 1

Which theorem states that every real symmetric matrix can be orthogonally diagonalized?

Question 2

Which real matrices are guaranteed to be orthogonally diagonalizable?

Question 3

In an orthogonal diagonalization $A=QDQ^T$, what is true about $Q$?

Question 4

In an orthogonal diagonalization $A=QDQ^T$, what do the diagonal entries of $D$ represent?

Question 5

For a real symmetric matrix, eigenvectors corresponding to distinct eigenvalues are what?