Ničelno-neničelni vzorci idempotentnih matrik : delo diplomskega seminarja

Zupan, Borut (author), Oblak, Polona (mentor)

V delu karakteriziramo kvadratne idempotentne ničelno-neničelne matrike z elementi iz množice $\{0, \ast\}$. Da bi identificirali vse take matrike, ta problem prevedemo na iskanje kvadratnih binarnih matrik nad poljem realnih števil, ki ta problem rešijo. Nato določimo največje število možnih neničelnih elementov v idempotentni ničelno-neničelni matriki z danim rangom.

• Language: Slovenian
• Keywords: ničelno-neničelne matrike, idempotentnost, binarne matrike, rang
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-131034
• UDC: 512
• COBISS.SI-ID: 77664771
• Publication date in RUL: 22.09.2021

Secondary language

• Language: English
• Title: Idempotent zero-nonzero patterns

Abstract

We first characterize square idempotent zero-nonzero patterns with elements from $\{0, \ast\}$. To identify these matrices, we convert this problem into characterizing square binary idempotent matrices over the real numbers. Next we determine maximal possible number of nonzero entries in indempotent zero-nonzero pattern with a given minimum rank.

• Keywords: zero-nonzero pattern, idempotence, binary matrix, rank