Back to Complex eigenvalues and eigenvectors

Exercise 8.11.2

Avg difficulty 3.0

I know a certain real $2\times 2$ -matrix $A$ . My matrix has complex eigenvalue $\lambda=1+2i$ and corresponding eigenvector $\mathbf{v}=\left[\begin{array}{c}1\\ i\end{array}\right]$ .

Find another eigenvalue and corresponding eigenvector of $A$ .
Diagonalize $A$ .
What is the secret matrix $A$ ?

Selinger, Matrix Theory and Linear Algebra, Eigenvalues, eigenvectors, and diagonalization, Complex eigenvalues and eigenvectors, Exercise 8.11.2

AI Tutor

Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.