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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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126–150 of 715 nodes
  • Definition of codomain of a linear transformation#23841
  • Definition of coefficient matrix of a linear system#23756
  • Definition of coefficients of a linear equation#23414
  • Definition of cofactor/submatrix of a matrix#23717
  • Definition of column rank of a matrix#23673
  • Definition of column space of a matrix#23875
  • Definition of column vector#23780
  • Definition of complement of a subspace#23975
  • Definition of composition of linear transformations#24023
  • Definition of conjugate of a matrix#23465
  • Definition of conjugate of a vector in C^n#23788
  • Definition of consistent linear system#23431
  • Definition of constant vector of a linear system#23757
  • Definition of coordinates relative to a given basis#23835
  • Definition of coordinate vector/mapping/representation relative to a given basis#23991
  • Definition of cross product#24121
  • Definition of determinant of a matrix as a cofactor expansion across the first row#23718
  • Definition of determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.#23724
  • Definition of diagonalizable linear transformation#24041
  • Definition of diagonalizable matrix#23611
  • Definition of diagonal matrix#23456
  • Definition of dimension of a vector space (or subspace)#23837
  • Definition of dimension of a vector space (or subspace) being finite or infinite#24009
  • Definition of direct sum of subspaces#23970
  • Definition of distance#23911
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  • Aspen Summer 2016 - Entanglement Matters#1213
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