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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1994 • Question 3

Question

Math 6310 • Algebra Fall 1994 • Question 3

  1. Define the elementary divisors of a square matrix \(M\) over the principal ideal domain \(R\).
  2. Calculate the elementary divisors of the matrix of integers \[ \begin {pmatrix} 4 & 6\\ 6 & 12 \end {pmatrix}. \]

Raw LaTeX

\begin{enumerate}
\item[(a)] Define the elementary divisors of a square matrix \(M\) over the principal ideal domain
\(R\).
\item[(b)] Calculate the elementary divisors of the matrix of integers
\[
  \begin{pmatrix}
  4 & 6\\
  6 & 12
  \end{pmatrix}.
\]
\end{enumerate}

Topic Tags

Ideals and Quotient Rings Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization Modules over PIDs Smith Normal Form and Invariant Factors