Hi(adsbygoogle = window.adsbygoogle || []).push({});

This is more of a math question but in the context of Quantum Mechanics, hence I posted it here. Suppose I have a matrix A of order 3x3 with three eigenvalues: 0, 0, 5. I am supposed to find the diagonalizing matrix for A.

I know that in general, if P denotes the matrix of eigenvectors of A, then [itex]PAP^{-1}[/itex] will be a diagonal matrix.

In my particular example, for the eigenvalue 0,

AX = 0

gives infinitely many solutions for X, so the eigenvector with eigenvalue 0 cannot be uniquely determined.

How do I diagonalize such a matrix?

Thanks in advance,

Cheers

Vivek

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

Dismiss Notice

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!

# Diagonalizing a square matrix with degenerate eigenvalues

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