The Hoffman-Wielandt inequality for quaternion matrices and quaternion matrix polynomials
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917002105323520 |
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| author | Basavaraju, Pallavi Hadimani, Shrinath Jayaraman, Sachindranath |
| author_facet | Basavaraju, Pallavi Hadimani, Shrinath Jayaraman, Sachindranath |
| contents | The purpose of this paper is to derive the Hoffman-Wielandt inequality and its
generalization for quaternion matrices. Diagonalizability of the block companion matrix
of certain quadratic (linear) quaternion matrix polynomials is brought out. As a
consequence, we prove that if $Q(λ)$ is another quadratic (linear) quaternion
matrix polynomial, then under certain conditions on the coefficients, a generalization of the
Hoffman-Wielandt inequality for their corresponding block companion matrices holds. We also prove
that if $P(λ)$ is a quaternion matrix polynomial with unitary coefficients, then any right
eigenvalue $λ_0$ of $P(λ)$ lies in the annular region $\frac{1}{2} < |λ_0| < 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07638 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Hoffman-Wielandt inequality for quaternion matrices and quaternion matrix polynomials Basavaraju, Pallavi Hadimani, Shrinath Jayaraman, Sachindranath Spectral Theory 15B33, 15A42, 15A18, 15A20, 12E15, 15A66 The purpose of this paper is to derive the Hoffman-Wielandt inequality and its generalization for quaternion matrices. Diagonalizability of the block companion matrix of certain quadratic (linear) quaternion matrix polynomials is brought out. As a consequence, we prove that if $Q(λ)$ is another quadratic (linear) quaternion matrix polynomial, then under certain conditions on the coefficients, a generalization of the Hoffman-Wielandt inequality for their corresponding block companion matrices holds. We also prove that if $P(λ)$ is a quaternion matrix polynomial with unitary coefficients, then any right eigenvalue $λ_0$ of $P(λ)$ lies in the annular region $\frac{1}{2} < |λ_0| < 2$. |
| title | The Hoffman-Wielandt inequality for quaternion matrices and quaternion matrix polynomials |
| topic | Spectral Theory 15B33, 15A42, 15A18, 15A20, 12E15, 15A66 |
| url | https://arxiv.org/abs/2302.07638 |