Basic question, I think, but I'm not sure. It is a step in a demonstration, so it would be nice if it were true.
True or false? Why? If A is a real, symmetric, nonsingular matrix, then xTAx≠0 for x≠0.
Homework Statement
Being T\in L(\mathbb{R}^n) a linear operador defined by T(x_1, ... ,x_n )=(x_1+...+x_n,...,x_1+...+x_n ), find all eigenvalues and eigenvectors of T.
Homework Equations
det(T-\lambda I)=0, Ax=\lambda x
The Attempt at a Solution
By checking n=1,2,3,4 I guess the...