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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.#24085
- Equivalence theorem for injective linear transformations: The inverse of T is a linear transformation on its range.#24078
- Equivalence theorem for injective linear transformations: The kernel of T is 0.#24081
- Equivalence theorem for injective linear transformations: The nullity of T is 0.#24080
- Equivalence theorem for injective linear transformations: The null space of T is 0.#24079
- Equivalence theorem for injective linear transformations: The rank of T is equals the number of columns in any matrix representation..#24084
- Equivalence theorem for injective linear transformations: The rank of T is n.#24083
- Equivalence theorem for injective linear transformations: T(x)=0 only for x=0.#24082
- Equivalence theorem for nonsingular matrices: the columns of A are a basis for R^n (or C^n).#23653
- Equivalence theorem for nonsingular matrices: the columns of A are linearly independent.#23651
- Equivalence theorem for nonsingular matrices: the columns of A span R^n (or C^n).#23649
- Equivalence theorem for nonsingular matrices: the determinant of A is nonzero.#23665
- Equivalence theorem for nonsingular matrices: the dimension of the column space of A is n.#23654
- Equivalence theorem for nonsingular matrices: the equation Ax=0 has only the trivial solution.#23647
- Equivalence theorem for nonsingular matrices: the equation Ax=b has a solution for all b.#23646
- Equivalence theorem for nonsingular matrices: the equation Ax=b has a unique solution for all b.#23645
- Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax has an inverse.#23663
- Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax is an isomorphism.#23664
- Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax is one-to-one/injective.#23661
- Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax is onto/surjective.#23662
- Equivalence theorem for nonsingular matrices: the matrix A does not have 0 as an eigenvalue.#23669
- Equivalence theorem for nonsingular matrices: the matrix A has a left inverse.#23658
- Equivalence theorem for nonsingular matrices: the matrix A has an inverse.#23657
- Equivalence theorem for nonsingular matrices: the matrix A has a right inverse.#23659
- Equivalence theorem for nonsingular matrices: the matrix A has rank n.#23666
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