# 60 KAM Mathematical Colloquium

## TOPICS FROM COMBINATORIAL MATRIX THEORY

čtvrtek 11. května 2006 ve 12:20, posluchárna S5, druhé patro
KAM MFF UK
Malostranske nam. 25
118 00 Praha 1

## Abstract

In combinatorial matrix theory, one -in the simplest cases- considers either the distribution of zeros and nonzeros, or, in the real case, the distribution of positive, zero, and negative entries with respect to properties of matrix characteristics. There are, of course, other problems which have combinatorial character such as completion problems, elimination problems, etc.

We intend to present examples, some classical, some recent, of such results. It is natural that terms like undirected or directed graphs, bipartite graphs, signed graphs, etc. are appropriate in the description.

Among the topics, we mention the following:

1. Characterization of sign-patterns of inverse-positive matrices.
2. Characterization of sign-patterns of symmetric positive semidefinite matrices of corank one.
3. Intrinsic matrix products and factorizations.
4. Application to sign-nonsingular matrices.

## O přednášejícím

Profesora Miroslava Fiedlera neni treba ceske a slovenske matematicke verejnosti dlouze predstavovat. Pripomenme pouze, ze za sve dlouhe matematicke drahy se venoval teorii matic, linearni algebre, kombinatorice a teorii grafu a je autorem 5 knih a pres 180 vedeckych publikaci, jejichz pocet stale narusta. Jeho prace o vlastnich cislech grafu a zvlaste pak o Fiedlerove cisle lambda_2 se staly svetozname a jadrem jak teoretickych tak praktickych aplikaci. M. Fiedlerovi se za jeho praci dostalo uznani doma i v zahranici (Narodni cena, zlata medaile B. Bolzana, Cena H. Schneidera atd.). Byl dlouholetym predsedou ceskoslovenskeho a posleze ceskeho matematickeho komitetu, je cestnym clenem JCMF a clenem Ucene spolecnosti CR. V soucasnosti je editorem 5 mezinarodnich casopisu (z toho dvou jako cestny editor) a dlouholetym vedoucim editorem casopisu Czechoslovak Mathematical Journal. Prof. Fiedler prednese kolokvium venovane hlavni oblasti jeho rozsahle vedecke cinnosti.