Using Lagrange Polynomial to Compute Eigenspace

Definition

1. If $T$ is diagonalizable, we can compute the projection $E_i$ using the Lagrange Polynomial.
2. For $1\le j\le k$
3. Then, $p(x):={\Pi }_{i\ne j}\frac{(x-c_i)}{c_j-c_i}=\frac{(x-c_1)\dots (x-c_{j-1})(c-c_{j+1})\dots (x-c_k)}{(c_j-c_1)\dots (c_j-c_{j-1})(c_j-c_{j+1})\dots (c_j-c_k)}$
4. Then, $p_j(T)=E_j$