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On the maximal numerical range of some matrices

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2018-02-21

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Hamed, Ali Nosherwan
Spitkovsky, Ilya Matveevich

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Abstract

The maximal numerical rangeW0(A) of a matrixAis the (regular) numerical rangeW(B) of its compressionBonto the eigenspaceLofA∗Acorresponding to its maximal eigenvalue. So, alwaysW0(A)⊆W(A). Conditions under whichW0(A) has a non-empty intersection with the boundary ofW(A) are established, in particular, whenW0(A) =W(A). ThesetW0(A) is also described explicitly for matrices unitarily similar to direct sums of 2-by-2 blocks, and some insight into thebehavior ofW0(A) is provided whenLhas codimension one.

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https://hdl.handle.net/1885/733811476

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ANU Research Publications

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The Electronic Journal of Linear Algebra

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Journal article

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10.13001/1081-3810.3774

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