Chapter 2: Operations with Matrices

Trace

The trace of a matrix is just the sum of all of its diagonal elements. In terms of components, $$\mathrm{tr}(A)=\sum_i A_{ii}.$$ For example, if $$A=\left(\begin{array}{ccc} 1&2&3\\ 4&5&6\\ 7&8&9\\ \end{array}\right) $$ then $$\mathrm{tr}(A)=1+5+9=15.$$

Try it for yourself by computing $$\mathrm{tr}\left(\begin{array}{ccc} 1&34&5\\ 23&5&98\\ 132&7&9\\ \end{array} \right).$$


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