# Find a Matrix given a characteristic equation

How I can compute a matrix given the characteristic equation ?

All I found are references and functions that do the exact opposite, but I know the characteristic equation and I need the corresponding matrix / linear system .

for example the equation is :

$$( \lambda - \alpha ) ( \lambda - \beta ) = 0$$

I have to find the matrix A such that A itself maps to those polynomials .

Replay

This gives you the entries for such a matrix:

mat = {{a, b}, {c, d}};
SolveAlways[CharacteristicPolynomial[mat, λ] == (λ - α) (λ - β), λ]



However, it is probably preferable to choose mat such that it has only as many unknowns as the matrix dimension.

Category: matrix Time: 2016-07-28 Views: 0

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