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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

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# Diagonalizing a square matrix with degenerate eigenvalues

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