Talk:Defective matrix

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Field: Algebra

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:
• ${\displaystyle {\begin{bmatrix}1&1\\0&1\end{bmatrix}}}$ is invertible and defective
• ${\displaystyle {\begin{bmatrix}0&0\\0&1\end{bmatrix}}}$ 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)

Merge

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

Singular example

Hi Plastikspork. I see you reverted my change to the simple example. Could you explain your reasoning? You said "It was already a simple example". My objection to the original example was that it was singular (not simple), which I thought might be confusing.--catslash (talk) 00:18, 21 April 2010 (UTC)

I didn't revert your example entirely. I just changed it to something a bit more simple. I agree that the singular one wasn't so good. This article actually needs a bit of help. There is no mention of the connection to the Jordan canonical form and the defective property of a general Jordan block. Thanks for your help. Plastikspork ―Œ(talk) 01:58, 21 April 2010 (UTC)
Sorry, I didn't look very carefully at what you'd done - too hasty with my indignation. --catslash (talk) 09:07, 21 April 2010 (UTC)