KnowraSymmetric matrixLinked fromLinked fromThe 9 pages that link to Symmetric matrix, each with the reason it gives.All 9Broader topic 1Related 5Narrower topic 1Compared with 2Quadratic formRelated: Its entries encode the coefficients of a quadratic form over fields of characteristic not two.EigenvectorRelated: Its eigenvectors can be chosen as an orthonormal basis.Orthogonal matrixCompared with: Symmetry constrains a matrix differently from the inverse-transpose condition.Square matrixBroader topic: It is a structured subclass with real eigenvalues and orthogonal eigenvectors.Positive-definite matrixNarrower topic: Symmetry ensures real eigenvalues and makes the quadratic-form definition equivalent to familiar tests.Diagonal matrixRelated: Symmetry guarantees orthogonal diagonalization over the real numbers, even when the matrix is not already diagonal.Sylvester's law of inertiaRelated: Every real quadratic form can be represented by a symmetric matrix.Triangular matrixCompared with: Symmetry reflects entries across the diagonal rather than requiring one triangular half to vanish.Eigenvalues and eigenvectorsRelated: Its eigenvalues are real and its eigenvectors can be chosen orthonormal, simplifying the general case.