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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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The standard inner product of a vector with itself is non-negative

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The standard inner product of a vector with itself is 0 only for the 0 vectorClose match
The inner product of a vector with itself is the square of its norm/length.Close match
The standard inner product on R^n is commutative.Close match
Definition of inner productClose match
The standard inner product on C^n can be written as the product of a vector and the adjoint of a vector.Close match
The standard inner product on R^n commutes with (real) scalar multiplication.Close match
Norm and lengthClose match
Inner products in coordinate spacesClose match
The standard inner product on R^n (or C^n) distributes over addition.Close match
Inner productsClose match
Definition of length/norm of a vectorClose match
The complex inner product is conjugate symmetricClose match
The Cauchy-Schwarz inequalityClose match
Complex inner products conjugate scalars in the first argumentClose match
Definition of inner/dot product on R^nClose match
The standard inner product on R^n can be written as the product of a vector and the transpose of a vector.Close match
Definition of inner/dot product on C^nClose match
Definition of inner product spaceClose match
The triangle inequalityClose match
The Cauchy–Schwarz inequalityClose match

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