Definition:Trace (Linear Algebra)

Matrix
Let $A = (a_{ij})_{1\leq i,j \leq n}$ be a matrix.

The trace of $A$ is:


 * $\displaystyle \operatorname{tr}(A) = \sum_{i = 1}^n a_{ii}$

Linear Transformation
Let $V$ be a vector space.

Let $A : V \to V$ be a linear transformation of $V$.

The trace of $A$ is the trace of the matrix of $A$ with respect to some basis.