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Suppose that $A$ is singular, is $A^3 + A^2 + A$ singular as well?

  • 1
    I would think of that this way: $A$ is a linear transformation from $\mathbb R^n$ to $\mathbb R^n$ that squashes at least one dimension. If you apply this transformation multiple times, it will still squash that dimension. Therefore, that sum is also singular.2012-11-18
  • 0
    Since already answered, let's just add for completeness than any polynomial $p(A)$ is also singular.2012-11-18
  • 3
    At least if $p$ does not have a constant term.2012-11-19

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