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  • Subspaces associated to a linear transformation

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  • The range/image of a linear transformation is a subspace.
  • The inverse image of a subspace under a linear transformation is a subspace.
  • Definition of kernel/null space of linear transformation
  • The kernel/null space of a linear transformation is a subspace
  • Definition of generalized kernel/null space of linear transformation
  • Any vector space is the direct sum of the generalized kernel and gneralized range of a linear transformation on that space.
  • The kernels of powers of a linear transformation form an ascending chain
  • The range spaces of powers of a linear transformation form a descending chain
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  1. Any vector space is the direct sum of the generalized kernel and gneralized range of a linear transformation on that space.

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  • Definition of row equivalent matrices#23479
  • Definition of row operations on a matrix#23475
  • Definition of row reduce a matrix#23545
  • Definition of row space of a matrix#23880
  • Definition of scalar#23778
  • Definition of scalar multiple of a linear transformation#24017
  • Definition of Schur triangulation#23633
  • Definition of similarity transform#23637
  • Definition of similar matrices#23635
  • Definition of singular matrix (not nonsingular)#23643
  • Definition of singular value decomposition (SVD)#23623
  • Definition of size of a matrix#23451
  • Definition of size of a vector#23782
  • Definition of skew-symmetric matrix#23579
  • Definition of solution set of a system of linear equations#23418
  • Definition of solution to a linear equation#23415
  • Definition of solution to a system of linear equations#23417
  • Definition of solution vector of a linear system#23758
  • Definition of spanning/generating set for a space or subspace#23978
  • Definition of span of a set of vectors#23805
  • 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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