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Numerical Analysis - Matrix Norm equalities.

  • Thread starter PillT
  • Start date
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1. Homework Statement

Determine constants c and C that do not depend on vector x. For this to be true:

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Use this result and the definition of matrix norms to determine constants k and K so that:

4OxcY.jpg



2. Homework Equations

rHtKys.jpg


3. The Attempt at a Solution


I've done half of this problem. For c and C it was not hard. I found that if c = 1/n (n being the number of terms in the vector) and C = 1 the statement holds true.

The second half on the other hand has me stumped. The infinity norm and the one-norm only seem to share one term, due to one being the max row sum and the other being the max column sum. Can anyone give me any direction?

Thanks.
 

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