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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2022 • Question 5

Question

Math 6310 • Algebra Spring 2022 • Question 5

Let \(M\) be a \(5\times 5\) matrix over the complex numbers \(\mathbb {C}\), such that the eigenvectors of \(M\), along with the zero vector, form a two-dimensional vector subspace of \(\mathbb {C}^{5}\). Determine the possible Jordan forms of \(M\).

Raw LaTeX

Let \(M\) be a \(5\times5\) matrix over the complex numbers \(\mathbb{C}\), such that the eigenvectors of \(M\), along with the zero
vector, form a two-dimensional vector subspace of \(\mathbb{C}^{5}\). Determine the possible Jordan forms of \(M\).

Topic Tags

Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization