You are Here: Home >< Maths

Do all diagonal matricies have distinct eigenvalues? watch

1. Do all diagonal matrices have to have distinct eigenvalues?
2. (Original post by zakwilce)
Do all diagonal matrices have to have distinct eigenvalues?
3. (Original post by zakwilce)
Do all diagonal matrices have to have distinct eigenvalues?
Not sure what you mean exactly. Expand on it.
4. (Original post by RDKGames)
Not sure what you mean exactly. Expand on it.
Been given a maths question which just says "a diagonal matrix must have distinct eigenvalues, true or false" not really much to go off of.
5. (Original post by zakwilce)
Been given a maths question which just says "a diagonal matrix must have distinct eigenvalues, true or false" not really much to go off of.
Well, can you find a matrix whose eigenvalues repeat at least once?
6. (Original post by zakwilce)
Do all diagonal matrices have to have distinct eigenvalues?
A diagonalised matrix has entries in the leading diagonal corresponding to the eigenvalues of the original matrix.

No, matrixes with repeated eigenvalues can be diagonalizable, an obvious example is the Identity matrix.

Now it is sufficiently true that the set of matrices are diagonalizable over F if the eigenvalues are distinct, but the converse is not a true statement (it is not a necessary condition), so eigenvalues don't have to be distinct for the matrices to be diagonalizable, as above.
7. (Original post by NotNotBatman)
A diagonalised matrix has entries in the leading diagonal corresponding to the eigenvalues of the original matrix.
Let’s not completely give away the answer right from the bat, no matter how short it may be.

Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 13, 2018
Today on TSR

2,243

students online now

Exam discussions

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants