A diagonalizable matrix ?

by @ancient-tree · difficulty 9/100

Algebra

Status: Unreviewed

Unreviewed. Fresh or lightly reviewed. Read it, try it, improve it.
Improve this problemSee revisions

Is the matrix (1101)\left(\begin{array}{ll} 1 & 1 \\ 0 & 1 \end{array}\right) diagonalizable ?

Proofs

1

The most useful proof appears first. At 3 useful votes, it is marked community accepted.

Proof by @ancient-tree

0 useful votes

The only eigenvalue of this matrix is 1 (with algebraic multiplicity 2). So if it was diagonalizable, it would be similar to the identity matrix : (1101)=P(1001)P−1=(1001)\left(\begin{array}{ll} 1 & 1 \\ 0 & 1 \end{array}\right)=P\left(\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right) P^{-1}=\left(\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right)
which is a contradiction.

Discuss proof · 0

Discussion

Sign in to start this problem and unlock the discussion after 24h.