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The trace $tr (A)$ as the sum of the diagonal entries

Definition

For a square matrix $A = (a_{i j}) \in M_{n} (F)$ , its trace is the sum of its diagonal entries,

$tr (A) : = \sum_{i \in n} a_{i i} .$

For $n = 0$ , this is the empty sum, so the unique empty matrix has trace $0$ .

Depends on

Used by

Trace is a linear functional on Mₙ(F) Proposition
For A∈ M_m× n(F) and B∈ M_n× m(F), tr(AB)=tr(BA) Theorem

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 51 results over 16 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources

S. Axler, Linear Algebra Done Right, 4th ed., Definition 8.47 (standard reference, not scraped)

The trace tr⁡(A)tr(A) as the sum of the diagonal entries