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  • Subspaces

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  • Definition of intersection of subspaces
  • Definition of direct sum of subspaces
  • Definition of the 0/trivial subspace
  • Definition of subspace
  • Definition of subspace spanned by a set of a set of vectors
  • Definition of 0/trivial subspace
  • A nonempty subset of a vector space is a subspace if and only if it is closed under linear combinations
  • The intersection of subspaces is a subspace
  • Definition of sum of subspaces
  • The sum of subspaces is a subspace
  • The dimension of a direct sum of subspaces is the sum of the dimensions of the subspaces.
  • Definition of independent subspaces
  • A vector can be written uniquely as a linear combination of vectors from independent subspaces.
  • The union of bases from independent subspaces is a basis for the space.
  • Definition of complement of a subspace
  • Theorem characterizing when a space is the direct sum of two subspaces
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  1. The union of bases from independent subspaces is a basis for the space.

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76–100 of 718 nodes
  • Axioms of a vector space#23798
  • Bases#23828
  • Basic properties#23957
  • Basic properties of linear transformations#23863
  • Basic terminology#23412
  • Basic terminology and notation#23448
  • Basis exchange using a nonzero coordinate#23990
  • Block matrices#23567
  • Canonical forms of matrices#23608
  • Change of coordinates matrices are invertible#23998
  • Characteristic and minimal polynomials#23699
  • Choosing factorizations and understanding numerical error#37115
  • C^n is a vector space.#24098
  • Cofactors#23716
  • Commuting diagonalizable and nilpotent decomposition over the complex numbers#23585
  • Complex inner products conjugate scalars in the first argument#23900
  • Composition#24022
  • Condition number measures relative sensitivity#23750
  • Conjugating by a change of coordinates matrix converts matrix representations with respect to different bases.#23999
  • Conjugation#23464
  • Container for Linear Algebra#24123
  • Coordinates#23989
  • Coordinate vector spaces#23776
  • Cramer's rule#23722
  • Definition and terminology#23954
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1–4 of 4 public trees
  • Aspen Summer 2016 - Entanglement Matters#1213
  • Container for Linear Algebra#24123
  • Math#23168
  • Test Flight Problem Set#23151

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