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  • Inner products in coordinate spaces

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  • Definition of inner/dot product on R^n
  • Definition of inner/dot product on C^n
  • The standard inner product on R^n is commutative.
  • The complex inner product is conjugate symmetric
  • The standard inner product on R^n commutes with (real) scalar multiplication.
  • Complex inner products conjugate scalars in the first argument
  • The standard inner product on R^n (or C^n) distributes over addition.
  • The standard inner product of a vector with itself is non-negative
  • The standard inner product of a vector with itself is 0 only for the 0 vector
  • The standard inner product on R^n can be written as the product of a vector and the transpose of a vector.
  • The standard inner product on C^n can be written as the product of a vector and the adjoint of a vector.
  • A matrix turns into its adjoint when moved to the other side of the standard inner product on C^n.
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  1. Complex inner products conjugate scalars in the first argument

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  • 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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  • Aspen Summer 2016 - Entanglement Matters#1213
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