# Theory

### Algebraic Representation of Vectors

Helena Dedic

It is important that you learn to use symbols for vector, magnitude of a vector and component of a vector. Further, it is important to use these symbols when appropriate. In different texts or in different domains (e.g., physics, linear algebra etc.) these symbols may vary and you should be prepared to recognize different conventions. In your textbook and on this site the symbols are in the first row. The second row shows alternative symbols that physics texts often use. The third row shows the symbols for the same concepts that you will learn in linear algebra.

domain             vector           magnitude              component

physics               A               A                    ${\displaystyle A_{x}}$
physics               ${\displaystyle {\bar {A}}}$               A                    ${\displaystyle A_{x}}$
linear algebra        ${\displaystyle {\bar {a}}}$              ${\displaystyle \parallel {\bar {a}}\parallel }$                   ${\displaystyle a_{x}}$


Be aware that it is incorrect to write an equation:

${\displaystyle {\bar {A}}=3}$


but it is correct to write

${\displaystyle A_{x}=3}$