Hamed, Ali NosherwanSpitkovsky, Ilya Matveevich2026-06-152026-06-15Bibtex:hamed2018maximalORCID:/0009-0005-1151-7800/work/217370405https://hdl.handle.net/1885/733811476The 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.Supported in part by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi.16en©2018 The authors2018-02-2110.13001/1081-3810.377485055735860