Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1996 • Question 7

Question

Math 6310 • Algebra Fall 1996 • Question 7

Prove the Cayley-Hamilton Theorem (the theorem that states that for every matrix \(A\) we have \(f(A)=0\), where \(f(X)\) is the characteristic polynomial of \(A\)).

Raw LaTeX

Prove the Cayley-Hamilton Theorem (the theorem that states that for every matrix \(A\) we have
\(f(A)=0\), where \(f(X)\) is the characteristic polynomial of \(A\)).

Topic Tags

Galois Groups of Polynomials Irreducible Polynomials Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization Polynomial Rings and Ring Homomorphism Kernels