Wszystkie pola: Drazin inverse - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: The Drazin inverse of a class of partitioned matrices
Autorzy:: Kanan, Asmaa M.
Powiązania:: https://bibliotekanauki.pl/articles/1030682.pdf
Data publikacji:: 2020
Wydawca:: Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:: Drazin inverse
Partitioned matrix
Rank
Trace of matrix
Opis:: In this work, we give the representations of the Drazin inverse for the partitioned matrix [■(A_1&A_2@O&A_3 )] with A_1 and A_3 square and singular under the conditions that rank(A_1 )=rank(A_3 )=1, Trace(A_1)≠0 and Trace(A_3)≠0, and then we give the representations of the Drazin inverse for the partitioned EP matrix [■(A_1&A_2@A_3&A_4 )] with A_1 is square and non-singular under the conditions that rank(A_1 )=rank([■(A_1&A_2@A_3&A_4 )]), and [■(A_1&A_2@A_3&A_4 )]=[■(I@P)] A_1 [■(I&Q)] where P=A_3 〖A_1〗^(-1) and Q= 〖A_1〗^(-1) A_2. Also, we give the representations of the Drazin inverse for the partitioned matrix [■(A_1&A_2@A_3&A_4 )] with A_1 square and singular under the conditions that rank(A_1 )=rank([■(A_1&A_2@A_3&A_4 )])=1, Trace([■(A_1&A_2@A_3&A_4 )])≠0.
Źródło:: World Scientific News; 2020, 139, 2; 173-185
2392-2192
Pojawia się w:: World Scientific News
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Solution of linear systems of differential equations with singular constant coefficients by the Drazin inverse of matrices
Autorzy:: Kanan, Asmaa M.
Hassan, Khadija
Powiązania:: https://bibliotekanauki.pl/articles/1046563.pdf
Data publikacji:: 2019
Wydawca:: Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:: Drazin inverse
Index
Singular differential equations
Opis:: Let A ,B be n×n matrices of complex numbers. Let G a vector-valued function of the real variable t. A and B may both be singular, rank(A) = 1, and the trac of A is not equal zero. The linear system of differential equations Ax^' (t)+Bx(t)=G(t) is studied using the Drazin inverse A^D of A, and a new matrix K∈C^(n×n). In this paper, we obtain a new closed form for the general solution of the differential system when the system is tractable.
Źródło:: World Scientific News; 2019, 137; 229-236
2392-2192
Pojawia się w:: World Scientific News
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Solutions of a class of singular linear systems of difference equations. Part 1
Autorzy:: Kanan, Asmaa M.
Powiązania:: https://bibliotekanauki.pl/articles/1030103.pdf
Data publikacji:: 2020
Wydawca:: Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:: Drazin inverse
Rank
Singular difference equations
Opis:: We extend results of Campbell, Meyer, Jr. and Rose of applications of the Drazine inverse to linear systems of differential equations with singular constant coefficients to solutions of linear systems of difference equations A x_(n+1)+B x_n= f_n ,n≥0 when A and B are m×m complex matrices and may both singular, under conditions that rank(A)=1 and trace of A is not equal zero. f_n is an arbitrary function in C^m, and x_n∈C^m. We give a new closed form for all solutions of those systems when they are tractable, using the theory of the Drazin inverse, and a matrix K∈C^(m×m).
Źródło:: World Scientific News; 2020, 143; 53-66
2392-2192
Pojawia się w:: World Scientific News
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Solutions of a class of singular linear systems of difference equations. Part 2
Autorzy:: Kanan, Asmaa M.
Powiązania:: https://bibliotekanauki.pl/articles/1030133.pdf
Data publikacji:: 2020
Wydawca:: Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:: Drazin inverse
Moore-Penrose generalized inverse
Singular linear difference systems
Opis:: We extend results of Campbell of the linear systems of differential equations A x ̇+ Bx=f when A and B are rectangular, and results of Kanan of solution of a class of singular linear systems of difference equations A x_(n+1)+ Bx_n=f_n when A and B are square, to such systems of difference equations when A and B are rectangular. Explicit solutions of the last one are derived for several cases. One such is, when the matrix (λA+B) is one-to-one, another case is when such matrix is onto, for a scalar λ∈C. Also, explicit solutions are derived for the case that A is onto, and for the case that B is onto.
Źródło:: World Scientific News; 2020, 143; 127-138
2392-2192
Pojawia się w:: World Scientific News
Dostawca treści:: Biblioteka Nauki

Artykuł

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