---- > [!definition] Definition. ([[trace of a linear operator]]) > The **trace** of a [[linear operator]] $T$ is defined as the sum of the [[eigenvalue]]s of $T$, repeated according to their multiplicities. > [!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 > ```