Inner and Outer Product of Matrix

Inner Product:

The inner product of two vectors u and v in the complex space, denoted as [html][/html] generates a complex as the output. The inner product must satisfy the following properties:

1. Linearity: [html](+v|c>) = w+v
2. Symmetry: [html](u|v) = (v|u)*
3. Positivity: [html] ≥ 0 for |u> ≠ 0

Outer Product:

The outer product between u and v is written as: