Existence of matrices with prescribed entries.
Ion Zaballa (1986)
Extracta Mathematicae
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Ion Zaballa (1986)
Extracta Mathematicae
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R. Ben Taher, M. Rachidi (2015)
Special Matrices
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We present a constructive procedure for establishing explicit formulas of the constituents matrices. Our approach is based on the tools and techniques from the theory of generalized Fibonacci sequences. Some connections with other results are supplied. Furthermore,we manage to provide tractable expressions for the matrix functions, and for illustration purposes we establish compact formulas for both the matrix logarithm and the matrix pth root. Some examples are also provided. ...
Michael Cox, Kevin N. Vander Meulen, Adam Van Tuyl, Joseph Voskamp (2024)
Czechoslovak Mathematical Journal
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The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition...
Miroslav Fiedler (1977)
Mathematica Slovaca
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H. S. Thurston (1939)
Compositio Mathematica
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Li, Hsuan-Chu, Chen, Young-Ming, Tan, Eng-Tjioe (2009)
Integers
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Lee, Moon Ho, Feng, Gui-Liang, Chen, Zhu (2008)
Mathematical Problems in Engineering
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Nobuyuki Tamura, Yatsuka Nakamura (2007)
Formalized Mathematics
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In this paper the classic theory of matrices of real elements (see e.g. [12], [13]) is developed. We prove selected equations that have been proved previously for matrices of field elements. Similarly, we introduce in this special context the determinant of a matrix, the identity and zero matrices, and the inverse matrix. The new concept discussed in the case of matrices of real numbers is the property of matrices as operators acting on finite sequences of real numbers from both sides....