Total positiv matrices
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 (mackscheidt@mathb.rwth-aachen.de). Please also write in your mail whether you want to get charged the proseminar as such one or as a seminar.
Talks
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10/10/2019: Definitionen sowie Aussagen zur Minorenberechnung (Da-Un J.)
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10/10/2019: Konstruktion einiger total positiver Matrizen (Jonas S.)
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10/17/2019: Der Rang total positiver Matrizen (Yannic R.)
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10/24/2019: Ungleichungen für Determinanten (Jonas K.)
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10/31/2019: Feketes Lemma (Moritz B.)
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11/07/2019: Dichtheit total positiver Matrizen (Jazmin R.)
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11/14/2019: Totale Positivität für Dreiecksmatrizen (Leon S.)
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11/21/2019: LDU-Zerlegung (Julian H.)
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11/28/2019: Verfeinerung der LDU-Zerlegung (Michael S.)
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12/05/2019: Ein Kriterium für totale Positivität (Annika B.)
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12/12/2019: Beispiele (Antonia B.)
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12/19/2019: Vorzeichenwechsel bei Multiplikation mit total positiven Matrizen (Dilay B.)
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01/09/2020: Oszillationsmatrizen und das Gantmacher-Krein-Kriterium (León v. E.)
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01/16/2020: Eigenwerte von Untermatrizen (Kathleen D.)
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01/23/2020: Eigenwerte und Eigenvektoren total positiver Matrizen (Nevar M.)
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01/30/2020: Total positive Matrizen und Kombinatorik (Da-Un J.)