Complex Vectors

Vectors with complex components

Since

Is not defined if or are a zero vector, they must be non-zero.

Complex vectors mostly behave like real vectors

For

We compute

Meaning , and

Complex Inner Product

Definition

Note that in non-engineering math, the conjugate is placed on the second variable

It follows that the definition of the magnitude for complex vectors is also different:

Also

Properties

Let and . Then:

  1. (if and only if, zero vector)
  5. (Cauchy-Schwarz Inequality)
  6. (Triangle Inequality)