Definition:Trace (Linear Algebra)

This page is about Trace in the context of Linear Algebra. For other uses, see Trace.

Definition

Matrix

Let $A = \sqbrk a_n$ be a square matrix of order $n$.

The trace of $A$ is:

$\ds \map \tr A = \sum_{i \mathop = 1}^n a_{ii}$

Linear Operator

Let $V$ be a vector space.

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

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