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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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A matrix turns into its adjoint when moved to the other side of the standard inner product on C^n.

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Matrix adjoint is an involution.Close match
The adjoint of a matrix-scalar product is the product of the adjoint and the conjugate.Close match
Definition of adjoint (conjugate transpose)Close match
Transpose and adjointClose 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 adjoint of a product of matrices is the product of the adjoints in reverse order.Close match
Definition of transpose of a matrixClose match
Matrix transpose is an involution.Close match
The transpose of a product of matrices is the product of the transposes in reverse order.Close match
Transpose commutes with scalar multiplication.Close match
Matrix-vector productsClose match
Matrix transpose commutes with matrix inverse.Close match
The conjugate of a matrix-scalar product is the product of the conjugates.Close match
The conjugate of the transpose is the transpose of the conjugate.Close match
Matrix-vector product is associativeClose match
The inverse of a matrix can be expressed in terms of its matrix of cofactors.Close match
The conjugate of a product of matrices is the product of the conjugates.Close match
The transpose of a sum of matrices is the sum of the transposes.Close match
The adjoint of a sum is the sum of the adjoints.Close match
Definition of adjugate/classical adjoint of a matrixClose match

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