For some matrix A:
- A is symmetric ⇔ A = A'
- A is positive definite ⇔ for every non-zero vector x, x'Ax > 0
- A is non-singular ⇔ A is invertible ⇔ detA≠0 ⇔ there exists B such that AB = BA = I
- A is a distance matrix ⇔ A is symmetric and diag(A) = 0
- A is non-singular ⇒ AA' is positive definite
- A is symmetric ⇒ AA is positive definite