Problem 615. Nilpotent matrix

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Solution 416264

Submitted on 10 Mar 2014 by Jon

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3 Comments

3 Comments

Shahnewaz Shuva on 14 Mar 2024

How is this in general true?

Christian Schröder on 14 Mar 2024

It isn't. For instance, rcond(hilb(10)) is less than 1e-12, but hilb(10) is not nilpotent.

Christian Schröder on 16 Mar 2024

As an addendum, this remains untrue even if you ignore floating-point issues and test (mathematically, rather than programmatically) whether rcond(A) is equal to 0. The matrix A=[1 0; 0 0] has rcond(A) equal to zero, but it is not nilpotent.

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