What set of properties does a matrix have to have in order for all its pairs of distinct eigenvectors $x$ and $y$ to have $x^Ty=0?$
91636
Are all eigenvectors, of any matrix, always orthogonal?
19649
A question about the proof of "a symmetric matrix has real eigenvalues".
141628
How did the equation $|A- \lambda I| = 0$ came for finding Eigen values of a Matrix
41932
Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
115296
Under what conditions does a matrix $A$ have a square root?
127719
Is the matrix $R$ in the $QR$ decomposition unique?
85581
Matrices commute if and only if they share a common basis of eigenvectors?
53993
Can Eigenvalues[] and Eigenvectors[] be assumed to return the same ordering?
22222
Properties of zero-diagonal symmetric matrices
39112
Does a correlation matrix of two variables always have the same eigenvectors?
66241
What can the eigenvalues of unitary matrices tell us?
156868
Why is finding $M$ eigenvectors on smaller matrix valid?
24454
The relationship between the eigenvalues of matrices $XY$ and $YX$
126337
Eigenvalues in orthogonal matrices
117293
sufficient and necessary conditions for matrix to be diagonalize or triangular
72541
Is the matrix diagonalizable for all values of t?
86125
If $A$ is idempotent, then the eigenvalues of $A$ are $0$ or $1$