Link Search Menu Expand Document
Linear Algebra

Homework 14 - Eigenvalues and eigenvectors over different fields

  1. Find the eigenspaces of the matrix \(A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}\) over $\mathbb{C}$.

  2. Find the eigenspaces of the matrix \(A = \begin{pmatrix} 1 & 1 \\ -1 & 1 \end{pmatrix}\) over $\mathbb{C}$.

  3. Show the complex numbers are an $\mathbb{R}$-vector space. What is its dimension over $\mathbb{R}$? For $z \in \mathbb{C}$, multiplication by $z$ is linear transformation of this vector space. Find a matrix representation for this linear transformation.