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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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  1. Equivalence theorem for injective linear transformations: The rank of T is equals the number of columns in any matrix representation..

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  • Definition of row equivalent matrices#23479
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  • Definition of singular matrix (not nonsingular)#23643
  • Definition of singular value decomposition (SVD)#23623
  • Definition of size of a matrix#23451
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  • Definition of square matrix#23454
  • Definition of subspace#23812
  • Definition of subspace spanned by a set of a set of vectors#23813
  • Definition of sum of linear transformations#24015
  • Definition of sum of matrices#23462
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