Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $A$ be an $n \times n$ matrix with complex entries. Pick out the true statements.

  1. $A$ is always similar to an upper-triangular matrix.
  2. $A$ is always similar to a diagonal matrix.
  3. $A$ is similar to a block diagonal matrix, with each diagonal block of size strictly less than $n$, provided $A$ has at least $2$ distinct eigenvalues.

I have solved $1$ & $2$. $1$ is true and $2$ is false.

But I cannot find how to solve $3$. Can somebody help?

share|cite|improve this question

2 Answers 2

This is true and the a way to see this is to consider the Jordan normal form .

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.