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Equivalence theorems for injective transformations

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Definition of one-to-one/injective linear transformation
Equivalence theorem for injective linear transformations: The inverse of T is a linear transformation on its range.
Equivalence theorem for injective linear transformations: The null space of T is 0.
Equivalence theorem for injective linear transformations: The nullity of T is 0.
Equivalence theorem for injective linear transformations: The kernel of T is 0.
Equivalence theorem for injective linear transformations: T(x)=0 only for x=0.
Equivalence theorem for injective linear transformations: The rank of T is n.
Equivalence theorem for injective linear transformations: The rank of T is equals the number of columns in any matrix representation..
Equivalence theorem for injective linear transformations: The image of a basis for V is a basis for the range of T.
Equivalence theorem for injective linear transformations: The columns of the matrix of T are linearly independent.

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Equivalence theorem for injective linear transformations: The null space of T is 0.

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Equivalence theorem for injective linear transformations: The kernel of T is 0.Close match
Equivalence theorem for injective linear transformations: T(x)=0 only for x=0.Close match
Equivalence theorem for injective linear transformations: The nullity of T is 0.Close match
Equivalence theorem for injective linear transformations: The inverse of T is a linear transformation on its range.Close match
Equivalence theorems for injective transformationsClose match
Equivalence theorem for injective linear transformations: The columns of the matrix of T are linearly independent.Close match
Equivalence theorem for injective linear transformations: The rank of T is n.Close match
Equivalence theorem for injective linear transformations: The image of a basis for V is a basis for the range of T.Close match
The kernel/null space of a linear transformation is a subspaceClose match
Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax is one-to-one/injective.Close match
Definition of kernel/null space of linear transformationClose match
Definition of kernel of linear transformationClose match
Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax is an isomorphism.Close match
Equivalence theorem for injective linear transformations: The rank of T is equals the number of columns in any matrix representation..Close match
Definition of nullity of a linear transformationClose match
A linear transformation is injective on its generalized range space.Close match
A linear transformation maps 0 to 0.Close match
Equivalence theorem for nonsingular matrices: the null space of the matrix A is {0}.Close match
A linear transformation is invertible if and only if it is injective and surjectiveClose match
Definition of generalized kernel/null space of linear transformationClose match

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