Consider the linear system $Ax = b$, where $A$ is known and you are given the following Matlab outputs:
norm(A-A') = 9.3e-16 min(eig(A)) = 1.3e-7 max(eig(A)) = 2.7e+6
I am wondering if it possible to determine if the matrix $A$ is symmetric.
A square matrix, $A$, is symmetric iff $A=A^T$ (where there transpose of a matrix $A$ is denoted by $A'$ in the Matlab outputs). If $A$ is symmetric, we expect $A-A'=0$. In the Matlab output, the norm used is the $2$-norm by default.
I am wondering what can be deduced by knowing norm$(A-A')$, or more conventionally, $\|A-A^T\|_2$.