06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun... more 06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.İlk bölümde matrisler ve bazı özel tipli matrislerle ilgili kısa bir literatür bilgisi verilmektedir.. İkinci bölümde bazı temel kavram ve özellikler verilmektedir. Üçüncü bölümde idempotent ve tripotent matrislerin tanımları verilip özellikleri ayrıntılı olarak incelenmektedir. Dördüncü bölümde literatürdeki, iki değişmeli tripotent matrisin lineer bileşimleri için 9 terimli ayrık idemotent ayrışım veren, bir çalışma incelenmektedir. Beşinci bölümde n tane değişmeli tripotent matristen elde edilen lineer bileşim için bir 3^n terimli ayrık idempotent ayrışım olduğu gösterildi ve böylece önceki bölümde elde edilen sonuçlar genelleştirildi. Ayrıca değişmeli...
Let Xi, i = 1, 2, ..., m, be diagonalizable matrices that mutually commute. This paper provides a... more Let Xi, i = 1, 2, ..., m, be diagonalizable matrices that mutually commute. This paper provides a combinatorial method to handle the problem when a linear combination matrix X = m i=1 ciXi is a matrix such that σ(X) ⊆ {λ1, λ2, ..., λn}, where ci, i = 1, 2, ..., m, are nonzero complex scalars and σ(X) denotes the spectrum of the matrix X. If the spectra of matrices X and Xi, i = 1, 2, ..., m, are chosen as subsets of some particular sets, then this problem is equivalent to the problem of characterizing all situations in which a linear combination of some commuting special types of matrices, e.g. the matrices such that A k = A, k = 2, 3, ..., is also a special type of matrix. The method developed in this note makes it possible to solve such characterization problems for linear combinations of finitely many special types of matrices. Moreover, the method is illustrated by considering the problem, which is one of the open problems left in [Linear Algebra Appl. 437 (2012) 2091-2109], of ...
The uniqueness of the sum of the elements of finite subsets of the odd or even indexed Fibonacci ... more The uniqueness of the sum of the elements of finite subsets of the odd or even indexed Fibonacci and Lucas sequences are proved. Moreover, it is shown that the odd or even indexed Fibonacci and Lucas sequences are superincreasing sequences. Furthermore, by utilizing the uniqueness properties established a new cryptology method is presented and exemplified.
We propose an algorithm, which is based on the method given by Kişi and Özdemir in [Math Commun, ... more We propose an algorithm, which is based on the method given by Kişi and Özdemir in [Math Commun, 23 (2018) 61], to handle the problem of when a linear combination matrix X=∑i=1mciXiX = \sum\nolimits_{i = 1}^m {{c_i}{X_i}} is a matrix such that its spectrum is a subset of a particular set, where ci, i = 1, 2, ..., m, are nonzero scalars and Xi, i = 1, 2, ..., m, are mutually commuting diagonalizable matrices. Besides, Mathematica implementation codes of the algorithm are also provided. The problems of characterizing all situations in which a linear combination of some special matrices, e.g. the matrices that coincide with some of their powers, is also a special matrix can easily be solved via the algorithm by choosing of the spectra of the matrices X and Xi, i = 1, 2, ..., m, as subsets of some particular sets. Nine of the open problems in the literature are solved by utilizing the algorithm. The results of the four of them, i.e. cubicity of linear combinations of two commuting cubic...
Let $X_i$, $i=1,2,...,m$, be diagonalizable matrices that mutually commute. This paper provides ... more Let $X_i$, $i=1,2,...,m$, be diagonalizable matrices that mutually commute. This paper provides a combinatorial method to handle the problem of when a linear combination matrix $X=\sum_{i=1}^{m}c_iX_i$ is a matrix such that $\sigma(X)\subseteq\{\lambda_1, \lambda_2,..., \lambda_{n}\}$, where $c_i$, $i=1,2,...,m$, are nonzero complex scalars and $\sigma(X)$ denotes the spectrum of the matrix $X$. If the spectra of the matrices $X$ and $X_i$, $i=1,2,...,m$, are chosen as subsets of some particular sets, then this problem is equivalent to the problem of characterizing all situations in which a linear combination of some commuting special types of matrices, e.g. the matrices such that $A^k=A$, $k=2,3,...$, is also a special type of matrix. The method developed in this note makes it possible to solve such characterization problems for the linear combinations of finitely many special types of matrices. Moreover, the method is illustrated by considering the problem, which is one of the op...
ABSTRACT This corrigendum provides the missing results of the paper in the title and also correct... more ABSTRACT This corrigendum provides the missing results of the paper in the title and also corrects the misprints in it.
It has been established a 3 n-term disjoint idempotent decomposition (DID) for the linear combina... more It has been established a 3 n-term disjoint idempotent decomposition (DID) for the linear combinations produced from n ðP 2Þ commutative tripotent matrices, their products and their products of power 2 at most. The results obtained in this way generalize those in [Y. Tian, A disjoint idempotent decomposition for linear combinations produced from two commutative tripotent matrices and its applications, Linear Multilinear Algebra 59 (2011) 1237-1246]. Moreover, an algorithm to get a DID has been provided. Finally, a numerical example has been given to exemplify the results.
06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun... more 06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.İlk bölümde matrisler ve bazı özel tipli matrislerle ilgili kısa bir literatür bilgisi verilmektedir.. İkinci bölümde bazı temel kavram ve özellikler verilmektedir. Üçüncü bölümde idempotent ve tripotent matrislerin tanımları verilip özellikleri ayrıntılı olarak incelenmektedir. Dördüncü bölümde literatürdeki, iki değişmeli tripotent matrisin lineer bileşimleri için 9 terimli ayrık idemotent ayrışım veren, bir çalışma incelenmektedir. Beşinci bölümde n tane değişmeli tripotent matristen elde edilen lineer bileşim için bir 3^n terimli ayrık idempotent ayrışım olduğu gösterildi ve böylece önceki bölümde elde edilen sonuçlar genelleştirildi. Ayrıca değişmeli...
Let Xi, i = 1, 2, ..., m, be diagonalizable matrices that mutually commute. This paper provides a... more Let Xi, i = 1, 2, ..., m, be diagonalizable matrices that mutually commute. This paper provides a combinatorial method to handle the problem when a linear combination matrix X = m i=1 ciXi is a matrix such that σ(X) ⊆ {λ1, λ2, ..., λn}, where ci, i = 1, 2, ..., m, are nonzero complex scalars and σ(X) denotes the spectrum of the matrix X. If the spectra of matrices X and Xi, i = 1, 2, ..., m, are chosen as subsets of some particular sets, then this problem is equivalent to the problem of characterizing all situations in which a linear combination of some commuting special types of matrices, e.g. the matrices such that A k = A, k = 2, 3, ..., is also a special type of matrix. The method developed in this note makes it possible to solve such characterization problems for linear combinations of finitely many special types of matrices. Moreover, the method is illustrated by considering the problem, which is one of the open problems left in [Linear Algebra Appl. 437 (2012) 2091-2109], of ...
The uniqueness of the sum of the elements of finite subsets of the odd or even indexed Fibonacci ... more The uniqueness of the sum of the elements of finite subsets of the odd or even indexed Fibonacci and Lucas sequences are proved. Moreover, it is shown that the odd or even indexed Fibonacci and Lucas sequences are superincreasing sequences. Furthermore, by utilizing the uniqueness properties established a new cryptology method is presented and exemplified.
We propose an algorithm, which is based on the method given by Kişi and Özdemir in [Math Commun, ... more We propose an algorithm, which is based on the method given by Kişi and Özdemir in [Math Commun, 23 (2018) 61], to handle the problem of when a linear combination matrix X=∑i=1mciXiX = \sum\nolimits_{i = 1}^m {{c_i}{X_i}} is a matrix such that its spectrum is a subset of a particular set, where ci, i = 1, 2, ..., m, are nonzero scalars and Xi, i = 1, 2, ..., m, are mutually commuting diagonalizable matrices. Besides, Mathematica implementation codes of the algorithm are also provided. The problems of characterizing all situations in which a linear combination of some special matrices, e.g. the matrices that coincide with some of their powers, is also a special matrix can easily be solved via the algorithm by choosing of the spectra of the matrices X and Xi, i = 1, 2, ..., m, as subsets of some particular sets. Nine of the open problems in the literature are solved by utilizing the algorithm. The results of the four of them, i.e. cubicity of linear combinations of two commuting cubic...
Let $X_i$, $i=1,2,...,m$, be diagonalizable matrices that mutually commute. This paper provides ... more Let $X_i$, $i=1,2,...,m$, be diagonalizable matrices that mutually commute. This paper provides a combinatorial method to handle the problem of when a linear combination matrix $X=\sum_{i=1}^{m}c_iX_i$ is a matrix such that $\sigma(X)\subseteq\{\lambda_1, \lambda_2,..., \lambda_{n}\}$, where $c_i$, $i=1,2,...,m$, are nonzero complex scalars and $\sigma(X)$ denotes the spectrum of the matrix $X$. If the spectra of the matrices $X$ and $X_i$, $i=1,2,...,m$, are chosen as subsets of some particular sets, then this problem is equivalent to the problem of characterizing all situations in which a linear combination of some commuting special types of matrices, e.g. the matrices such that $A^k=A$, $k=2,3,...$, is also a special type of matrix. The method developed in this note makes it possible to solve such characterization problems for the linear combinations of finitely many special types of matrices. Moreover, the method is illustrated by considering the problem, which is one of the op...
ABSTRACT This corrigendum provides the missing results of the paper in the title and also correct... more ABSTRACT This corrigendum provides the missing results of the paper in the title and also corrects the misprints in it.
It has been established a 3 n-term disjoint idempotent decomposition (DID) for the linear combina... more It has been established a 3 n-term disjoint idempotent decomposition (DID) for the linear combinations produced from n ðP 2Þ commutative tripotent matrices, their products and their products of power 2 at most. The results obtained in this way generalize those in [Y. Tian, A disjoint idempotent decomposition for linear combinations produced from two commutative tripotent matrices and its applications, Linear Multilinear Algebra 59 (2011) 1237-1246]. Moreover, an algorithm to get a DID has been provided. Finally, a numerical example has been given to exemplify the results.
Uploads
Papers by emre kişi