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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2011 • Question 4

Question

Math 6310 • Algebra Spring 2011 • Question 4

For the matrix \[ A= \begin {pmatrix} 1 & 0 & 0\\ 0 & 0 & -2\\ 0 & 1 & 3 \end {pmatrix}, \] find:

  1. the rational canonical form over \(\mathbb {Q}\);
  2. the Jordan canonical form over \(\mathbb {C}\).

Raw LaTeX

For the matrix
\[
A=
\begin{pmatrix}
1 & 0 & 0\\
0 & 0 & -2\\
0 & 1 & 3
\end{pmatrix},
\]
find:
\begin{enumerate}
\item the rational canonical form over \(\mathbb{Q}\);
\item the Jordan canonical form over \(\mathbb{C}\).
\end{enumerate}

Topic Tags

Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization