query: why is algebraic multiplicity always equal to the geometric multiplicity of distinct eigen values corresponding to Symmetric matrices?
positive_passages.docid: 21571
positive_passages.text: Why are real symmetric matrices diagonalizable?
negative_passages.docid: 53993
negative_passages.text: Can Eigenvalues[] and Eigenvectors[] be assumed to return the same ordering?
negative_passages.docid: 66995
negative_passages.text: Why is a projection matrix symmetric?
negative_passages.docid: 116539
negative_passages.text: Eigenvalues of matrix satisfying $A^2 = A$
negative_passages.docid: 40154
negative_passages.text: Finding the dimension of real symmetric matrices with trace zero
negative_passages.docid: 57731
negative_passages.text: Can commuting matrices $X,Y$ always be written as polynomials of some matrix $A$?
negative_passages.docid: 144145
negative_passages.text: Symmetric $3\times 3$ Matrices - Base matrix
negative_passages.docid: 93531
negative_passages.text: Do commuting matrices share the same eigenvectors?
negative_passages.docid: 40478
negative_passages.text: If $C$ commutes with certain matrices $A$ and $B$, why is $C$ a scalar multiple of the identity?
negative_passages.docid: 90576
negative_passages.text: Symmetric matrix eigenvalues
negative_passages.docid: 18282
negative_passages.text: Finding the minimal polynomial, the eigenvalues, and the characteristic polynomial of $T(A)=A+A^t$
negative_passages.docid: 98656
negative_passages.text: Geometric multiplicity of the largest eigenvalue
negative_passages.docid: 44632
negative_passages.text: eigenvalues of symbolic Hermitian 3X3 matrix
negative_passages.docid: 17391
negative_passages.text: Diagonalisation and characteristic polynomial
negative_passages.docid: 102192
negative_passages.text: Can someone explain geometric multiplicity?
negative_passages.docid: 109675
negative_passages.text: Finite sum of eigenspaces (with distinct eigenvalues) is a direct sum
negative_passages.docid: 28584
negative_passages.text: Eigenvalues and eigenspaces of AB