Find the projectors of matrix A
(I am not sure how to write it in matrix form here so I have written out each row of the matrix)
Row 1 : [ 2 1 1]
Row 2: [ 2 3 2]
Row 3: [ 1 1 2]
A theorem in my text book says the Lagrange interpolation polynomial hi(A) = the projectors Ei
The Attempt at a Solution
If my understanding is correct, then all I need is the Lagrange interpolation polynomials for this matrix.
Do I have to first express this matrix in terms of a vandermonde matrix to get the fixed points?
I know how to find the Lagrange interpolation polynomials if I am given the fixed points.
I know that the second column of the vandermonde matrix gives you the fixed points.
I am not so sure as to how to express this matrix in terms of a vandermonde matrix.