Inner products in coordinate spaces
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Children
- 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 standard inner product on C^n is anticommutative.
- The standard inner product on R^n commutes with (real) scalar multiplication.
- The standard inner product on C^n commutes/anticommutes with scalar multiplication.
- 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.