# Bra-ket Notation in Quantum Mechanics

## Bra Notation:

In linear algebra both column vectors and row vectors are used. The Dirac notation provides a symbol called a bra. It represents a row vector. The bras correspond to the kets `|0>` and `|a>` are:

```<0| = (1 0)
<1| = (0 1)
```

In a complex vector space V, every ket has a unique bra. The bras corresponding to a ket are obtained by taking the conjugate transpose of the ket (and vice versa). A bra `<u|` acting on a vector v turns it into a complex number c, this can be written as:

```<u|: v → c
```

## Ket Notation:

A vector v in a complex vector space V is denoted by a ket.

```|v>ε V
```

A ket is analogous to a column vector. Since the vector space is complex, all terms in a column vector are complex numbers.