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Keywords:
finite dimensional vector space; monotonic norm; absolute norm; inner pro\-duct norm
finite dimensional vector space; monotonic norm; absolute norm; inner pro\-duct norm
Summary:
Let $\Bbb K$ be the field of real or complex numbers. In this note we characterize all inner product norms $p_1,\ldots ,p_m$ on $\Bbb K^n$ for which the norm $x\longmapsto \max \{p_1(x),\ldots ,p_m(x)\}$ on $\Bbb K^n$ is monotonic.
References:
[1] Bauer F.L., Stoer J., Witzgall C.: Absolute and monotonic norms. Numer. Math. 3 (1961), 257-264. MR 0130104 | Zbl 0111.01602
[2] Horn R.A., Johnson C.R.: Matrix Analysis. Cambridge University Press, New York, 1985. MR 0832183 | Zbl 0801.15001
[3] Johnson C.R., Nylen P.: Monotonicity properties of norms. Linear Algebra Appl. 148 (1991), 43-58. MR 1090752 | Zbl 0717.15015
[4] Lavrič B.: Monotonicity and $ ^*$orthant-monotonicity of certain maximum norms. Linear Algebra Appl. 367 (2003), 29-36. MR 1976908 | Zbl 1038.15017
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