Υπολογισμός υποοριζουσών πινάκων στάθμισης W(n,n-1) με μηδενικά στη διαγώνιο

Postgraduate Thesis uoadl:1320565 710 Read counter

Unit:
Τομέας Μαθηματικής Ανάλυσης
Library of the School of Science
Deposit date:
2011-08-29
Year:
2011
Author:
Καραπιπέρη Άννα
Supervisors info:
Επ. Καθηγήτρια Μαριλένα Μητρούλη, Καθηγητής Βασίλης Δουγαλής, Αν. Καθηγητής Σωτήρης Νοτάρης
Original Title:
Υπολογισμός υποοριζουσών πινάκων στάθμισης W(n,n-1) με μηδενικά στη διαγώνιο
Languages:
Greek
Summary:
In several applications in mathematical sciences is required the computation
of the determinants and minors of matrices. The direct approach for evaluating
all the principal minors of a matrix by applying LU factorizations entails a
remarkable time complexity. Thus, analytical formulas will be useful to be
derived whenever it is possible. When we have matrices of special structure as
weighing matrices, this can be achieved.
In the present master thesis we concentrate our study on the evaluation of
minors for weighing matrices W(n, n-1) with zeros on the diagonal.
Specifically, we present known results for the evaluation of minors for
weighing matrices W(n, n-k), where n is even and kand we prove analogous propositions for weighing matrices W(n, n-1) with zeros
on the diagonal. Furthermore, for this specific category of matrices, we prove
the existence of an analytical formula for the evaluation of minors of order
n-r, where ntool of the first approach is the Determinant Simplification Theorem, while the
second one uses the orthogonality of the rows/columns.
Keywords:
Weighing matrices, Determinant–minors evaluation, Hadamard-equivalence, Schur complement, Determinant Simplification Theorem
Index:
No
Number of index pages:
0
Contains images:
No
Number of references:
18
Number of pages:
i, 62
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