Quantitative Finance

# Eigenvalues and Eigenvectors

Find the eigenvalues of the matrix $A = \begin{pmatrix} 8 & 0 & 0 \\6 & 6 & 11 \\ 1 & 0 & 1 \end{pmatrix}.$

What is the sum of eigenvalues of the transformation matrix $A = \begin{pmatrix} 8 & 2 \\ 2 & 8 \end{pmatrix}?$

Given the transformation matrix $A = \begin{pmatrix} 5 & 4 \\ 4 & 5 \end{pmatrix},$ which of the following are the eigenvectors of $A?$

Which of the following are the eigenvectors of the transformation matrix $A = \begin{pmatrix} 8 & 4 \\ 1 & 5 \end{pmatrix}?$

Which of the following can't be an eigenvector of the transformation matrix $A = \begin{pmatrix} 8 & 0 & 0 \\ 3 & 5 & 0 \\ 3 & 2 & 3 \end{pmatrix}?$

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