There are these questions in the book that ask us to find the Dimension of a particular space. Do I just find a basis for the space, and then the number of elements in that basis is the dimension for the space? Or is there some trick to finding the dimension? Thanks!(adsbygoogle = window.adsbygoogle || []).push({});

-----------

For example, the first one the book asks is: Find the dimension of 2x2 matricies. So a basis for 2x2 matricies is the following set:

[tex]\left\{\left(\begin{array}{cc}1&0\\0&0\end{array}\right), \left(\begin{array}{cc}0&1\\0&0\end{array}\right), \left(\begin{array}{cc}0&0\\1&0\end{array}\right), \left(\begin{array}{cc}0&0\\0&1\end{array}\right)\right\}[/tex]

And this basis has 4 elements, so the dimension of 2x2 matricies is 4.

---------

Is that basically how these problems go? Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Dimension - Linear Algebra

**Physics Forums | Science Articles, Homework Help, Discussion**