Principal Values and Principal Subspaces of Two Subspaces of Vector Spaces with Inner Product
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916623991963648 |
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| author | Risteski, Ice B. Trenčevski, Kostadin G. |
| author_facet | Risteski, Ice B. Trenčevski, Kostadin G. |
| contents | In this paper is studied the problem concerning the angle between two subspaces of arbitrary dimensions in Euclidean space $E_{n}$. It is proven that the angle between two subspaces is equal to the angle between their orthogonal subspaces. Using the eigenvalues and eigenvectors of corresponding matrix representations, there are introduced principal values and principal subspaces. Their geometrical interpretation is also given together with the canonical representation of the two subspaces. The canonical matrix for the two subspaces is introduced and its properties of duality are obtained. Here obtained results expand the classic results given in [1,2]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Principal Values and Principal Subspaces of Two Subspaces of Vector Spaces with Inner Product Risteski, Ice B. Trenčevski, Kostadin G. General Mathematics 15A03, 51N20 In this paper is studied the problem concerning the angle between two subspaces of arbitrary dimensions in Euclidean space $E_{n}$. It is proven that the angle between two subspaces is equal to the angle between their orthogonal subspaces. Using the eigenvalues and eigenvectors of corresponding matrix representations, there are introduced principal values and principal subspaces. Their geometrical interpretation is also given together with the canonical representation of the two subspaces. The canonical matrix for the two subspaces is introduced and its properties of duality are obtained. Here obtained results expand the classic results given in [1,2]. |
| title | Principal Values and Principal Subspaces of Two Subspaces of Vector Spaces with Inner Product |
| topic | General Mathematics 15A03, 51N20 |
| url | https://arxiv.org/abs/2502.14877 |