MarkowChain&StationaryDistributionDef(FiniteMarkowChain).Let\(\Omega\)beafinitesetofstates,\(\forallx,y\in\Omega,P(x,y)\ge0\)beatransitionfunction,i.e.,\(\sum\limits_{y\in\Omega}P(x,y)=1.\)AfiniteMarkowchain

SVDDef(eigenvalue\eigenvector).Eigenvalue\(\lambda\)andeigenvector\(\bm{v}\)ofmatrix\(A\)satisfy$$A\bm{v}=\lambda\bm{v}.$$Lem1.Let\(M\in\mathbb{R}^{n\timesn}\)isasymmetricmatrix.Let\(\lambda_i\)and\(\bm{u}_i