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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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Complex inner products conjugate scalars in the first argument

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The complex inner product is conjugate symmetricClose match
The standard inner product on R^n commutes with (real) scalar multiplication.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
Inner products in coordinate spacesClose match
Definition of inner productClose match
Inner productsClose match
The standard inner product on R^n is commutative.Close match
The standard inner product of a vector with itself is 0 only for the 0 vectorClose match
Definition of inner/dot product on C^nClose match
The standard inner product on R^n (or C^n) distributes over addition.Close match
The adjoint of a matrix-scalar product is the product of the adjoint and the conjugate.Close match
The conjugate of a matrix-scalar product is the product of the conjugates.Close match
Matrix conjugation is an involution.Close match
A matrix turns into its adjoint when moved to the other side of the standard inner product on C^n.Close match
The standard inner product of a vector with itself is non-negativeClose match
Definition of inner product spaceClose 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 R^nClose match
The inner product of a vector with itself is the square of its norm/length.Close match
Matrix-vector product is associativeRelated

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