Symmetric positive definite matrix

$A$ is $m\times n$ matrix

Definition

• $A=A^T$ and $(\forall x\ne 0)x^{T}Ax>0$.
• For all $0<i<n$
  • Diagonal entries $a_{ii}>0$
  • Eigenvalues ${\lambda }_i>0$
  • Condition number $cond(A)=\frac{\max \lambda }{\min \lambda }$