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Subspaces associated to a linear transformation

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The kernels of powers of a linear transformation form an ascending chain
The range/image of a linear transformation is a subspace.
The inverse image of a subspace under a linear transformation is a subspace.
Definition of kernel/null space of linear transformation
The kernel/null space of a linear transformation is a subspace
Definition of generalized kernel/null space of linear transformation
Finite-dimensional Fitting decomposition into generalized kernel and range
The range spaces of powers of a linear transformation form a descending chain

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Definition of generalized kernel/null space of linear transformation

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Definition of kernel/null space of linear transformationClose match
Definition of kernel of linear transformationClose match
The kernel/null space of a linear transformation is a subspaceClose match
Finite-dimensional Fitting decomposition into generalized kernel and rangeClose match
Definition of generalized range space of a linear transformationClose match
A linear transformation is injective on its generalized range space.Close match
Definition of nullity of a linear transformationClose match
The kernels of powers of a linear transformation form an ascending chainClose match
Definition of nilpotent linear transformationClose match
Subspaces associated to a linear transformationClose match
Equivalence theorem for injective linear transformations: The null space of T is 0.Close match
Equivalence theorem for injective linear transformations: The kernel of T is 0.Close match
Definition of invariant subspace of a linear transformation.Close match
The rank plus the nullity of a linear transformation equals the dimension of the domain.Close match
An eigenspace of a matrix is a nontrivial subspace.Close match
Definition of matrix null space (right)Close match
Definition of matrix null space (left)Close match
Definition of 0/trivial subspaceRelated
Definition of the 0/trivial subspaceRelated
The inverse image of a subspace under a linear transformation is a subspace.Related

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