Column matrices play a special role in physics, where they are interpreted as vectors or states. To remind us of this uniqueness they have their own special notation; introduced by Dirac, called “bra-ket” notation. In bra-ket notation, a column matrix can be written $$\left|v\right> := \left(\begin{array}{c} a\\ b\\ c\\ \end{array}\right).$$ The adjoint of this vector is denoted $$\left<v\right| := \left(\left|1\right>\right)^\dagger =\left(\begin{array}{ccc} a^*&b^*&c^*\\ \end{array}\right).$$ As one quick application, if we take $\left|v\right>$ to be a 3-vector with components $a$, $b$, and $c$ as above, then the magnitude of the vector is $$\left<v|v\right> = \left(\begin{array}{ccc} a^*&b^*&c^*\\ \end{array}\right) \left(\begin{array}{c} a\\ b\\ c\\ \end{array}\right) = \left|a\right|^2+\left|b\right|^2+\left|c\right|^2$$ which is exactly the result expected. This property is one example of the overlap between linear algebra and vector analysis.