When is a matrix triangularizable

Notify me of new posts by email. This site uses Akismet to reduce spam. Learn how your comment data is processed. The list of linear algebra problems is available here. Enter your email address to subscribe to this blog and receive notifications of new posts by email. Email Address. Linear Algebra. Two Matrices with the Same Characteristic Polynomial. Diagonalize if Possible. Group Theory. How to Prove a Matrix is Nonsingular in 10 Seconds.

Nilpotent Matrix and Eigenvalues of the Matrix. Contents Problem 11 Hint. Proof of a. Related Question. Prove that every diagonalizable nilpotent matrix is the zero matrix.

Some of them may be the same. We give two solutions. Solution 1. If every trace of a power of a matrix is zero, then the matrix is nilpotent — Problems in Mathematics. Create a free Team What is Teams? Learn more. Ask Question. Asked 4 years, 2 months ago. Active 4 years, 2 months ago.

Viewed 6k times. What should I look for to prove if a matrix is triangularisable? What are the implications on its eigenvalues eigenvectors and eigenspaces? Leroy Leroy 3 3 silver badges 13 13 bronze badges. Add a comment. Active Oldest Votes. Trevor Gunn Trevor Gunn Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown.