Definition:Trace (Linear Algebra)/Matrix

Definition

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

The trace of $A$ is:

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

Using Einstein Summation Convention

The trace of $A$, using the Einstein summation convention, is:

$\map \tr A = a_{ii}$

Also see

• Results about traces of matrices can be found here.

Sources

• 1967: John D. Dixon: Problems in Group Theory ... (previous) ... (next): Introduction: Notation
• 1980: A.J.M. Spencer: Continuum Mechanics ... (previous) ... (next): $2.1$: Matrices: $(2.7)$
• 1998: Richard Kaye and Robert Wilson: Linear Algebra ... (previous) ... (next): Part $\text I$: Matrices and vector spaces: $1$ Matrices: $1.6$ Determinant and trace
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): trace