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Is an invariant subspace always spanned by a set of generalized eigenvectors?

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Non-orthogonal invariant subspaces

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An example for an invertible matrix with no $3$-dimensional invariant subspaces

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Does every eigenspace of the exterior power $\bigwedge^k A$ corresponds to an invariant subspace?

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189
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Invariant Subspaces and Orthogonality

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#linear-algebra #orthogonality #invariant-subspace
344
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On Minimal polynomial and Invariant subspace

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#linear-algebra #linear-transformations #minimal-polynomials #invariant-subspace
504
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How to see if a subspace is contained in another subspace?

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#linear-algebra #vectors #invariant-subspace
68
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Proving a property of a linear operator and its adjoint if they commute

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#linear-algebra #polynomials #invariant-subspace
677
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Linear Algebra - Invariant Subspaces in 2-dimensions

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Eigenvectors and invariant subspaces

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Kernel of a polynomial which divides the minimal polynomial

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#linear-algebra #linear-transformations #minimal-polynomials #invariant-subspace
403
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Does intersection of invariant subspace distribute over direct sum of invariant subspace found by minimal polynomial?

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#linear-algebra #linear-transformations #minimal-polynomials #direct-sum #invariant-subspace
394
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How to prove this theorem on diagonalizable operator on finite dimensional Vector space.

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#linear-algebra #vector-spaces #diagonalization #direct-sum #invariant-subspace
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$T \in \mathcal L (V)$ has no real eigenvalues. Prove that every subspace of $V$ invariant under $T$ has even dimension.

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Burnside's theorem on invariant subpaces

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