Total positiv matrices



Verity Mackscheidt



+49 241 80 97554



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.

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.)