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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 inverse of T is a linear transformation on its range.

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Equivalence theorem for injective linear transformations: The image of a basis for V is a basis for the range of T.Close match
Equivalence theorem for injective linear transformations: T(x)=0 only for x=0.Close 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
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Equivalence theorem for injective linear transformations: The rank of T is n.Close match
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