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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 0 only for the 0 vector

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The standard inner product of a vector with itself is non-negativeClose match
The standard inner product on R^n is commutative.Close 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 complex inner product is conjugate symmetricClose match
The standard inner product on R^n (or C^n) distributes over addition.Close match
Inner products in coordinate spacesClose match
The inner product of a vector with itself is the square of its norm/length.Close match
Definition of inner/dot product on C^nClose match
Complex inner products conjugate scalars in the first argumentClose match
The standard inner product on R^n commutes with (real) scalar multiplication.Close match
Definition of inner productClose match
Inner productsClose match
Norm and lengthClose match
The Cauchy-Schwarz inequalityClose match
The conjugate of a sum of vectors in C^n is the sum of the conjugatesClose 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
The 0 scalar multiplied by any vector equals the 0 vector.Close match
If the product of a vector and a scalar is 0Close match
The 0 vector is unique.Close match

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