(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant equations

A theorem in my text book says the Lagrange interpolation polynomial h_{i}(A) = the projectors E_{i}

3. 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.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Spectral Decomposition of a Matrix

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