If you need an accessible version of this item please contact JSTOR User Support

Every n × n Matrix Z with Real Spectrum Satisfies |Z - Z*| ≤ |Z + Z*| (log2 n + 0.038)

W. Kahan
Proceedings of the American Mathematical Society
Vol. 39, No. 2 (Jul., 1973), pp. 235-241
DOI: 10.2307/2039622
Stable URL: http://www.jstor.org/stable/2039622
Page Count: 7
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
Every n × n Matrix Z with Real Spectrum Satisfies |Z - Z*| ≤ |Z + Z*| (log2 n + 0.038)
Preview not available

Abstract

The title's inequality is proved for the operator bound-norm in a unitary space. An example is exhibited to show that the inequality cannot be improved by more than about 8% when n is large. The numerical range, of an n × n matrix Z with real spectrum, is then shown to be not arbitrarily different in shape from the spectrum.

Page Thumbnails

  • Thumbnail: Page 
235
    235
  • Thumbnail: Page 
236
    236
  • Thumbnail: Page 
237
    237
  • Thumbnail: Page 
238
    238
  • Thumbnail: Page 
239
    239
  • Thumbnail: Page 
240
    240
  • Thumbnail: Page 
241
    241