Demonstratio MathematicaGiven a square matrix AA, we are able to construct numerous equalities involving reasonable mixed operations of AA and its conjugate transpose A∗{A}^{\ast }, Moore-Penrose inverse A†{A}^{\dagger } and group inverse A#{A}^{\#}. Such kind of equalities can
Tian Yongge
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On Real Solutions of the Equation Φ\u3csup\u3e\u3cem\u3et\u3c/em\u3e\u3c/sup\u3e (\u3cem\u3eA\u3c/em\u3e) = 1/\u3cem\u3en\u3c/em\u3e J\u3csub\u3e\u3cem\u3en\u3c/em\u3e\u3c/sub\u3e [PDF]
, 2001 For a class of n × n-matrices, we get related real solutions to the matrix equation Φt (A) = 1/n Jn by generalizing the approach of and applying the results of Zhang, Yang, and Cao [SIAM J. Matrix Anal. Appl., 21 (1999), pp. 642–645].
Chen, Yuming
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Matrix equation representation of the convolution equation and its unique solvability
Special MatricesWe consider the convolution equation F*X=BF* X=B, where F∈R3×3F\in {{\mathbb{R}}}^{3\times 3} and B∈Rm×nB\in {{\mathbb{R}}}^{m\times n} are given and X∈Rm×nX\in {{\mathbb{R}}}^{m\times n} is to be determined. The convolution equation can be regarded as a
Satake Yuki +3 more
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Quadratic Approximation of Generalized Tribonacci Sequences
Discussiones Mathematicae - General Algebra and Applications, 2018 In this paper, we give quadratic approximation of generalized Tribonacci sequence {Vn}n≥0 defined by Vn = rVn−1 + sV n−2 + tV n−3 (n ≥ 3) and use this result to give the matrix form of the n-th power of a companion matrix of {Vn}n≥0. Then we re-prove the
Cerda-Morales Gamaliel
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Determinant Identities and the Geometry of Lines and Circles
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 The focus of this note is the nontrivial determinant identities which typically underlie the complex analytic proofs of all the results in the plane geometry of lines and circles.
Anghel Nicolae
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A new non-linear recurrence identity class for Horadam sequence terms. [PDF]
, 2018 We state, and prove by a succinct matrix method, a non-linear recurrence identity class for terms of the so called Horadam sequence. A particular instance was established (in equivalent form) over half a century ago by A.F.
Fennessey, Eric J., Larcombe, Peter J.
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Arithmetic, geometric, and harmonic means for accretive-dissipative matrices
, 2016 The concept of Loewner (partial) order for general complex matrices is introduced. After giving the definition of arithmetic, geometric, and harmonic mean for accretive-dissipative matrices, we study their basic properties.
Lin, Minghua
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Weak dual generalized inverse of a dual matrix and its applications. [PDF]
Heliyon, 2023 Li H, Wang H.
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Circulating miR-146b and miR-27b are efficient biomarkers for early diagnosis of Equidae osteoarthritis. [PDF]
Sci Rep, 2023 Yassin AM +5 more
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Weighted MP weak group inverse
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaTo extent the notion of the MP weak group inverse for square matrices, we introduce the concept of the weighted MP weak group inverse for rectangular matrices.
Mosić Dijana, Marovt Janko
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