(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose the A [tex]\in[/tex] M_{n X n}(F) has two distinct eigenvalues, [tex]\lambda[/tex]_{1}and [tex]\lambda[/tex]_{2}, and that dim(E_{[tex]\lambda[/tex]1}) = n -1. Prove A is diagonalizable.

2. Relevant equations

3. The attempt at a solution

1. The charac poly clearly splits because we have eigenvalues.

2. need to show m = dim (E).

Ok, we are given that dim(E_{[tex]\lambda[/tex]1}) = n - 1

we know multiplicity has to be 1 [tex]\leq[/tex] dim(E_{[tex]\lambda[/tex]1}) [tex]\leq[/tex] m.

so: 1 [tex]\leq[/tex] n - 1 [tex]\leq[/tex] m.

But im stuck now, not sure how to show that m = dim(E_{[tex]\lambda[/tex]})

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Diagonalizability of matrix

**Physics Forums | Science Articles, Homework Help, Discussion**