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Equivalence theorems for injective transformations
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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
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.
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 one-to-one/injective linear transformation

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Definition of invertible linear transformationClose match
Equivalence theorems for injective transformationsClose match
Definition of inverse of a linear transformationClose match
Definition of invertible/nonsingular linear transformationClose match
Definition of linear transformation/homomorphismClose match
Equivalence theorem for injective linear transformations: The inverse of T is a linear transformation on its range.Close match
Definition of onto/surjective linear transformationClose match
Definition of identity linear transformationClose match
Linear transformationsClose match
Definition of pre-image (of a point) under a linear transformationClose match
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
A linear transformation is invertible if and only if it is injective and surjectiveClose match
Equivalence theorem for injective linear transformations: The image of a basis for V is a basis for the range of T.Close match
Definition of domain of a linear transformationClose match
Non-example of a linear transformationClose match
Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax is one-to-one/injective.Close match
Definition of pre-image of linear transformationClose match
Equivalence theorem for injective linear transformations: The columns of the matrix of T are linearly independent.Close match
The inverse of an isomorphism is an isomorphism.Close match

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