[Turkmath:5664] IMBM Etkinliği: MSGSU Matematik Genel Seminerleri (8 Haziran, 15:00)

[İpek Tuvay]

Sayın liste üyeleri,

Bu haftanın seminerini, son zamanlarda yaşanılan olumsuz gelişmeler
nedeniyle IMBM'yi desteklemek amacıyla IMBM etkinliği olarak düzenliyoruz.
Seminerin detaylarını aşağıda bulabilirsiniz.

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*Tarih:* 8 Haziran 2022, 15:00

*Konuşmacı:* Semra Öztürk (ODTÜ)

*Başlık: *On m-th root of nilpotent matrices

*Özet:* This talk is based on the paper with the same title which
appeared in Electronic Journal of Linear Algebra, November 2021
it is dedicated to the memory of dear Professor Cem Tezer.

A new necessary and sufficient condition for the existence of an m-th root
of a nilpotent matrix in terms of the multiplicities of Jordan blocks is
obtained
and expressed as a system of linear equations with nonnegative integer
entries.
Thus, computation of the Jordan form of the m-th power of a nilpotent matrix
is reduced to a single matrix multiplication; conversely, the existence of
an m-th
root of a nilpotent matrix is reduced to the existence of a nonnegative
integer
solution to the corresponding system of linear equations. For a singular
matrix
having an m-th root with a pair of nilpotent Jordan blocks of sizes s and l,
a new m-th root is constructed by replacing that pair by another one of
sizes
s + i and l − i, for special s, l, i. If time permits we can state some
results for
the existence of m-th roots of A^k for a matrix A over an arbitrary field
that is
a sum of two commuting matrices where k ≥ t and t is the nilpotency of the
nilpotent part of A.

*Bağlantı: *
https://teams.microsoft.com/l/meetup-join/19%3a1eaca84648fa440e94bc4d7382675247%40thread.tacv2/1654451869477?context=%7b%22Tid%22%3a%22ddd5afa6-82d7-4e0e-b457-3000f5a23749%22%2c%22Oid%22%3a%22b11f2b28-e233-4b68-b781-77d2029695cb%22%7d
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*Gelecek konuşmalar için: *https://researchseminars.org/seminar/MSGSUMath

İpek Tuvay
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