Show that the eigenvectors corresponding to distinct eigenvalues of the symmetric matrix are orthogonal
18012
Eigenvectors of real symmetric matrices are orthogonal
56670
The intuition behind generalized eigenvectors
30882
Proving Invertibility and Eigenvalues
124583
A question about eigenvalues of $5\times5$ matrix
22222
Properties of zero-diagonal symmetric matrices
66500
Proving that orthogonal vectors are linearly independent
99600
Show that a 2x2 matrix A is symmetric positive definite if and only if A is symmetric, trace(A) > 0 and det(A) > 0
15417
Tricky problem on skew-symmetric matrices
88473
Proof that the trace of a matrix is the sum of its eigenvalues
128835
Compactness of the set of $n \times n$ orthogonal matrices
115467
Eigenvalues of Householder matrix
126337
Eigenvalues in orthogonal matrices
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
57318
Property of the conjugate transpose matrix with inner product
90964
Prove: symmetric positive definite matrix
98135
Show that the determinant of $A$ is equal to the product of its eigenvalues
6960
Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal