4 ms·
Recently read some nice articles on the companion matrix. One cool One: how to find the polynomial whose eigenvalues are the squares of those of some given po
by onos 4y ago
Recently read some nice articles on the companion matrix. One cool
One: how to find the polynomial whose eigenvalues are the squares of those of some given polynomial p? Ans: get the companion matrix for p, square it, and then get the characteristic polynomial for the squared matrix.
- sdenton4 4y agoYah, in short, any matrix operation where you can track the effect off the operation on the eigenvalues of the matrix will give you the same effect of polynomial roots. I used to work in algebraic combinatorics, which provides maps between important objects in algebra, combinatorics, and geometry, allowing us to apply theorems across the domains. You would often have dead obvious observations on one side which were very difficult to prove on another; eg 'This particular eigenvalue is a positive integer because it is also the dimension of a vector space."
- voldacar 4y ago>You would often have dead obvious observations on one side which were very difficult to prove on another; eg 'This particular eigenvalue is a positive integer because it is also the dimension of a vector space. This is interesting, could you give some other examples?