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Exercises

  1. [11K] Prerequisites:[11F].Let’s consider square matrices, i.e. n=m. We know from [11F] that norms β€–Aβ€–p,q are submultiplicative, that is β€–ABβ€–p,q≀‖Aβ€–p,qβ€–Aβ€–p,q.

    Show that the Frobenious norm is also submultiplicative.

    Note that for a submultiplicative norm we have that β€–Ak‖≀‖Aβ€–k for every natural k.

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