The Relationship between Similar Invariant Subspaces and Invariant Subspaces

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.