Total positiv matrices



Verity Mackscheidt



+49 241 80 92552



In the proseminar we treat the theory of total positive matrices. That are matrices whose minors are positive. We will consider topics such as:

- properties of total positive matrices

- creterions to determine total positivity

- examples

- different applications: factorisation, eigen values, combinatorics, ...

As main literature we will use the book "Totally positive matrices" of Allan Pinkus.

The proseminar also can be charged as a seminar. Each participant has to give a 45 minutes talk (charging as a seminar: 60 minutes talk) and additionally hand in an elaboration in LaTeX.

The seminar takes place on thursdays, 12.30pm. The room is usually the 5 (Rochusstr. 2-14, ground floor). However, on 10/24/2019 and on 12/05/2019 the proseminar takes place in SG 202 in the seminar building.

All talks are already distributed. The room for the seminar will be anounced on this webpage at a later date.

If you are interested in participation, please register in advance by mail to Verity Mackscheidt ( Please also write in your mail whether you want to get charged the proseminar as such one or as a seminar.



  • 10/10/2019: Definitionen sowie Aussagen zur Minorenberechnung (Da-Un J.)
  • 10/10/2019: Konstruktion einiger total positiver Matrizen (Jonas S.)
  • 10/17/2019: Der Rang total positiver Matrizen (Yannic R.)
  • 10/24/2019: Ungleichungen für Determinanten (Jonas K.)
  • 10/31/2019: Feketes Lemma (Moritz B.)
  • 11/07/2019: Dichtheit total positiver Matrizen (Jazmin R.)
  • 11/14/2019: Totale Positivität für Dreiecksmatrizen (Leon S.)
  • 11/21/2019: LDU-Zerlegung (Julian H.)
  • 11/28/2019: Verfeinerung der LDU-Zerlegung (Michael S.)
  • 12/05/2019: Ein Kriterium für totale Positivität (Annika B.)
  • 12/12/2019: Beispiele (Antonia B.)
  • 12/19/2019: Vorzeichenwechsel bei Multiplikation mit total positiven Matrizen (Dilay B.)
  • 01/09/2020: Oszillationsmatrizen und das Gantmacher-Krein-Kriterium (León v. E.)
  • 01/16/2020: Eigenwerte von Untermatrizen (Kathleen D.)
  • 01/23/2020: Eigenwerte und Eigenvektoren total positiver Matrizen (Nevar M.)
  • 01/30/2020: Total positive Matrizen und Kombinatorik (Da-Un J.)