Talk:Defective matrix

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[edit] Singular matrix?

How does this relate to a matrix being singular? —Ben FrantzDale 22:22, 21 December 2006 (UTC)

Not. All four combinations (invertible + diagonalizable, invertible + defective, singular + diagonalizable, singlar + defective) are possible. -- Jitse Niesen (talk) 14:48, 5 January 2007 (UTC)
Perhaps I'm overlooking something simple, but isn't a matrix singular iff its determinate is zero? The same appears from the examples to be true of a defective matrix. —Ben FrantzDale 14:53, 5 January 2007 (UTC)
It's dangerous to generalize from one example :) Here are some others:
  • \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix} is invertible and defective
  • \begin{bmatrix} 0 & 0 \\ 0 & 1 \end{bmatrix} is singular and not defective
A matrix is singular iff one of its eigenvalues is zero. Whether a matrix is defective has to do with the multiplicities of the eigenvalues, and not with the location of the eigenvalues. This explains why the properties are independent. -- Jitse Niesen (talk) 15:48, 5 January 2007 (UTC)
Aah. thanks. —Ben FrantzDale 16:16, 5 January 2007 (UTC)

[edit] Merge

I think this page should be merged with its antonym, diagonalizable matrix. -- Jitse Niesen (talk) 14:48, 5 January 2007 (UTC)