Invariant subspace

In mathematics, an invariant subspace of a linear mapping T : V → V from some vector space V to itself is a subspace W of V that is preserved by T; that is, T(W) ⊆ W.

Consider a linear mapping ${\displaystyle T}$ that transforms:

An invariant subspace ${\displaystyle W}$ of ${\displaystyle T}$ has the property that all vectors ${\displaystyle v\in W}$ are transformed by ${\displaystyle T}$ into vectors also contained in ${\displaystyle W}$. This can be stated as

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