MathDB

Call a polynomial

P(x_{1}, \ldots, x_{k})

good if there exist

2\times 2

real matrices

A_{1}, \ldots, A_{k}

such that

P(x_{1}, \ldots, x_{k}) = \det \left(\sum_{i=1}^{k}x_{i}A_{i}\right).

Find all values of

k

for which all homogeneous polynomials with

k

variables of degree 2 are good. (A polynomial is homogeneous if each term has the same total degree.)

Problem Statement