---- > [!definition] Definition. ([[trace of a matrix]]) > The **trace** of a [[matrix]] $A \in \mathbb{F}^{N \times N}$, denoted $\text{Tr }A$, is defined to be the sum of the [[diagonal]] entries of $A$. > [!justification] > We should expect that the [[trace of a linear operator]] equals that of any [[matrix]] representing it. This is verified here: [[trace of operator equals trace of matrix]]. ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```