The Relationship between Similar Invariant Subspaces and Invariant Subspaces

GU Wen; NI Junna

doi:10.6054/j.jscnun.2019072

Journal of South China Normal University (Natural Science Edition) > 2019 > 51(4): 100-103. > DOI: 10.6054/j.jscnun.2019072

GU Wen, NI Junna. The Relationship between Similar Invariant Subspaces and Invariant Subspaces[J]. Journal of South China Normal University (Natural Science Edition), 2019, 51(4): 100-103. DOI: 10.6054/j.jscnun.2019072

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The Relationship between Similar Invariant Subspaces and Invariant Subspaces

GU Wen,
NI Junna

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

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Received Date: September 19, 2018
Available Online: March 21, 2021

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Abstract

The concept of "similar invariant subspace" is defined and the relationship between similar invariant subspace and invariant subspace under the conditions of reversible linear transformation and general linear transformation is discussed. Using the theory of vector space, it is proved that similar invariant subspace is equivalent to invariant subspace under the condition of reversible linear transformation. Furthermore, it is proved that for a linear transformation σ of vector space V, if W is a similar invariant subspace, W must be an invariant subspace.
- similar invariant subspace,
- invariant subspace,
- linear transformation,
- vector space

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