Consider the quadratic forms \(f ( { \vec { x } } ) = x _ { 1 } ^ { 2 } + 2 x _ { 1 } x _ { 2 } + 3 x _ { 2 } ^ { 2 }\) and \(g ( \vec { x } ) = { 4 x _ { 1 } ^ { 2 } + 1 6 x _ { 1 } x _ { 2 } + }\) \(6 x _ { 2 } ^ { 2 }\) in \(\mathbb { R } ^ { 2 }\)
- Check if at least one of these forms is sign definite.
- Find the change of coordinates that reduces f (x) and g(x) to the diagonal form.