The state vectors \(\left|{+}\right\rangle \) and \(\left|{-}\right\rangle \) form an orthormal basis. Orthonormal bases have properties listed below.

For each property, write an equation that illustrates the property for both:

• The Cartesian basis vectors \(\hat{x}\), \(\hat{y}\), and \(\hat{z}\).
• The spin state vectors \(\left|{+}\right\rangle \) and \(\left|{-}\right\rangle \).

1. The elements are norm 1.

2. The elements are orthogonal.

3. The elements form a complete set. Any vector in the space can be written as a linear combination of the two.