Examples:: *[[Examples]]* Nonexamples:: *[[Nonexamples]]* Constructions:: *[[Constructions|Used in the construction of...]]* Generalizations:: *[[conjugate symmetric]]* Justifications and Intuition:: *[[Justifications and Intuition]]* Properties:: [[matrix of self-adjoint operator w.r.t. orthonormal bases is conjugate symmetric|over real numbers, the matrix of self-adjoint operator w.r.t. orthonormal bases is symmetric]] Sufficiencies:: *[[Sufficiencies]]* Equivalences:: [[Real Spectral Theorem|symmetric iff orthogonally diagonalizable]] ---- > [!definition] Definition. ([[symmetric matrix]]) > A [[matrix]] $M \in \rr^{n\times n}$ is called **symmetric** if $M=M^{\top}$. ---- #### ---- #### 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 > ```