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Definition of constant vector of a linear system
Definition of solution vector of a linear system
Definition of matrix representation of a linear system
Definition of domain of a linear transformation
Definition of codomain of a linear transformation
Definition of image (of a point) under a linear transformation
Definition of onto/surjective linear transformation
Definition of one-to-one/injective linear transformation
Definition of range of linear transformation
Definition of kernel of linear transformation
Definition of inverse of a linear transformation
Non-example of a linear transformation
A scalar multiple of a linear transformation is a linear transformation
Definition of augmented matrix (of a linear system)
Definition of coefficient matrix of a linear system
Definition of pre-image (of a point) under a linear transformation
Definition of invertible linear transformation
Definition of invertible/nonsingular linear transformation
Definition of linear transformation/homomorphism
Definition of identity linear transformation
Definition of sum of linear transformations
The sum of linear transformations is a linear transformation
Definition of scalar multiple of a linear transformation
Definition of pre-image of linear transformation
Definition of range of a linear transformation

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Definition of kernel of linear transformation

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Definition of kernel/null space of linear transformationClose match
Definition of generalized kernel/null space of linear transformationClose match
The kernel/null space of a linear transformation is a subspaceClose match
Equivalence theorem for injective linear transformations: The kernel of T is 0.Close match
Definition of nullity of a linear transformationClose match
Definition of pre-image of linear transformationClose match
Equivalence theorem for injective linear transformations: The null space of T is 0.Close match
Definition of domain of a linear transformationClose match
The rank plus the nullity of a linear transformation equals the dimension of the domain.Close match
The preimage of a vector is a translation of the kernel of the linear transformationClose match
Definition of pre-image (of a point) under a linear transformationClose match
Subspaces associated to a linear transformationClose match
The kernels of powers of a linear transformation form an ascending chainClose match
Definition of one-to-one/injective linear transformationClose match
Definition of linear transformation/homomorphismClose match
Linear transformationsClose match
Definition of invertible linear transformationClose match
Definition of range of a linear transformationClose match
Definition of codomain of a linear transformationClose match
Definition of range of linear transformationClose match

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