Extension and generalization properties of the weighted Minkowski inverse in a Minkowski space for an arbitrary matrix
The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, th...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Al-Zhour, Zeyad [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015transfer abstract |
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| Schlagwörter: |
Weighted singular value decomposition |
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| Umfang: |
8 |
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| Übergeordnetes Werk: |
Enthalten in: Growth and welfare implications of sector-specific innovations - Güner, İlhan ELSEVIER, 2022, an international journal, Amsterdam [u.a.] |
|---|---|
| Übergeordnetes Werk: |
volume:70 ; year:2015 ; number:5 ; pages:954-961 ; extent:8 |
| Links: |
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| DOI / URN: |
10.1016/j.camwa.2015.06.015 |
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ELV039805255 |
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| 520 | |a The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . | ||
| 520 | |a The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . | ||
| 650 | 7 | |a Weighted singular value decomposition |2 Elsevier | |
| 650 | 7 | |a Weighted Moore–Penrose inverse |2 Elsevier | |
| 650 | 7 | |a Weighted μ -symmetric |2 Elsevier | |
| 650 | 7 | |a Weighted Minkowski inverse |2 Elsevier | |
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10.1016/j.camwa.2015.06.015 doi GBVA2015013000019.pica (DE-627)ELV039805255 (ELSEVIER)S0898-1221(15)00301-6 DE-627 ger DE-627 rakwb eng 510 004 510 DE-600 004 DE-600 330 VZ 83.03 bkl 83.10 bkl Al-Zhour, Zeyad verfasserin aut Extension and generalization properties of the weighted Minkowski inverse in a Minkowski space for an arbitrary matrix 2015transfer abstract 8 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . Weighted singular value decomposition Elsevier Weighted Moore–Penrose inverse Elsevier Weighted μ -symmetric Elsevier Weighted Minkowski inverse Elsevier Enthalten in Elsevier Science Güner, İlhan ELSEVIER Growth and welfare implications of sector-specific innovations 2022 an international journal Amsterdam [u.a.] (DE-627)ELV008987521 volume:70 year:2015 number:5 pages:954-961 extent:8 https://doi.org/10.1016/j.camwa.2015.06.015 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 83.03 Methoden und Techniken der Volkswirtschaft VZ 83.10 Wirtschaftstheorie: Allgemeines VZ AR 70 2015 5 954-961 8 045F 510 |
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10.1016/j.camwa.2015.06.015 doi GBVA2015013000019.pica (DE-627)ELV039805255 (ELSEVIER)S0898-1221(15)00301-6 DE-627 ger DE-627 rakwb eng 510 004 510 DE-600 004 DE-600 330 VZ 83.03 bkl 83.10 bkl Al-Zhour, Zeyad verfasserin aut Extension and generalization properties of the weighted Minkowski inverse in a Minkowski space for an arbitrary matrix 2015transfer abstract 8 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . Weighted singular value decomposition Elsevier Weighted Moore–Penrose inverse Elsevier Weighted μ -symmetric Elsevier Weighted Minkowski inverse Elsevier Enthalten in Elsevier Science Güner, İlhan ELSEVIER Growth and welfare implications of sector-specific innovations 2022 an international journal Amsterdam [u.a.] (DE-627)ELV008987521 volume:70 year:2015 number:5 pages:954-961 extent:8 https://doi.org/10.1016/j.camwa.2015.06.015 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 83.03 Methoden und Techniken der Volkswirtschaft VZ 83.10 Wirtschaftstheorie: Allgemeines VZ AR 70 2015 5 954-961 8 045F 510 |
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10.1016/j.camwa.2015.06.015 doi GBVA2015013000019.pica (DE-627)ELV039805255 (ELSEVIER)S0898-1221(15)00301-6 DE-627 ger DE-627 rakwb eng 510 004 510 DE-600 004 DE-600 330 VZ 83.03 bkl 83.10 bkl Al-Zhour, Zeyad verfasserin aut Extension and generalization properties of the weighted Minkowski inverse in a Minkowski space for an arbitrary matrix 2015transfer abstract 8 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . Weighted singular value decomposition Elsevier Weighted Moore–Penrose inverse Elsevier Weighted μ -symmetric Elsevier Weighted Minkowski inverse Elsevier Enthalten in Elsevier Science Güner, İlhan ELSEVIER Growth and welfare implications of sector-specific innovations 2022 an international journal Amsterdam [u.a.] (DE-627)ELV008987521 volume:70 year:2015 number:5 pages:954-961 extent:8 https://doi.org/10.1016/j.camwa.2015.06.015 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 83.03 Methoden und Techniken der Volkswirtschaft VZ 83.10 Wirtschaftstheorie: Allgemeines VZ AR 70 2015 5 954-961 8 045F 510 |
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10.1016/j.camwa.2015.06.015 doi GBVA2015013000019.pica (DE-627)ELV039805255 (ELSEVIER)S0898-1221(15)00301-6 DE-627 ger DE-627 rakwb eng 510 004 510 DE-600 004 DE-600 330 VZ 83.03 bkl 83.10 bkl Al-Zhour, Zeyad verfasserin aut Extension and generalization properties of the weighted Minkowski inverse in a Minkowski space for an arbitrary matrix 2015transfer abstract 8 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . Weighted singular value decomposition Elsevier Weighted Moore–Penrose inverse Elsevier Weighted μ -symmetric Elsevier Weighted Minkowski inverse Elsevier Enthalten in Elsevier Science Güner, İlhan ELSEVIER Growth and welfare implications of sector-specific innovations 2022 an international journal Amsterdam [u.a.] (DE-627)ELV008987521 volume:70 year:2015 number:5 pages:954-961 extent:8 https://doi.org/10.1016/j.camwa.2015.06.015 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 83.03 Methoden und Techniken der Volkswirtschaft VZ 83.10 Wirtschaftstheorie: Allgemeines VZ AR 70 2015 5 954-961 8 045F 510 |
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10.1016/j.camwa.2015.06.015 doi GBVA2015013000019.pica (DE-627)ELV039805255 (ELSEVIER)S0898-1221(15)00301-6 DE-627 ger DE-627 rakwb eng 510 004 510 DE-600 004 DE-600 330 VZ 83.03 bkl 83.10 bkl Al-Zhour, Zeyad verfasserin aut Extension and generalization properties of the weighted Minkowski inverse in a Minkowski space for an arbitrary matrix 2015transfer abstract 8 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . Weighted singular value decomposition Elsevier Weighted Moore–Penrose inverse Elsevier Weighted μ -symmetric Elsevier Weighted Minkowski inverse Elsevier Enthalten in Elsevier Science Güner, İlhan ELSEVIER Growth and welfare implications of sector-specific innovations 2022 an international journal Amsterdam [u.a.] (DE-627)ELV008987521 volume:70 year:2015 number:5 pages:954-961 extent:8 https://doi.org/10.1016/j.camwa.2015.06.015 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 83.03 Methoden und Techniken der Volkswirtschaft VZ 83.10 Wirtschaftstheorie: Allgemeines VZ AR 70 2015 5 954-961 8 045F 510 |
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Enthalten in Growth and welfare implications of sector-specific innovations Amsterdam [u.a.] volume:70 year:2015 number:5 pages:954-961 extent:8 |
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extension and generalization properties of the weighted minkowski inverse in a minkowski space for an arbitrary matrix |
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Extension and generalization properties of the weighted Minkowski inverse in a Minkowski space for an arbitrary matrix |
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The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . |
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The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . |
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The weighted Minkowski inverse A M , N ⊕ ∈ M n , m related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . |
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Extension and generalization properties of the weighted Minkowski inverse in a Minkowski space for an arbitrary matrix |
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