## Minimal Gerschgorin sets for partitioned matrices III. Sharpness of boundaries and monotonicity as a function of the partition

Richard S. Varga and Alan Krautstengl

### Abstract

Making use, from the preceding paper, of the affirmative solution of the Spectral Conjecture, it is shown here that the general boundaries, of the minimal Gerschgorin sets for partitioned matrices, are sharp, and that monotonicity of these minimal Gerschgorin sets, as a function of the partitionings, is obtained. These results extend and sharpen an earlier paper from 1970 on this topic.

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### Key words

minimal Gerschgorin sets, partitioned matrices, monotonicity.

15A18.

### Links to the cited ETNA articles

 [4] Vol. 3 (1995), pp. 66-82 Alan Krautstengl and Richard S. Varga: Minimal Gerschgorin sets for partitioned matrices II. The spectral conjecture