Quadratic polynomial/R/2 variables/Standard form/2/Exercise

We consider the real quadratic polynomial

${}F=3X^{2}-5Y^{2}+7XY+4X-2Y+5\,$

with the pure-quadratic part

${}G=3X^{2}-5Y^{2}+7XY\,.$

a) Determine the standard form of ${}G$.

b) Determine an orthonormal basis such that ${}G$ is in standard form with respect to the new basis. Express the variables ${}X,Y$ with the new variables.

c) Express ${}F$ in the variables of the new orthonormal basis.

d) Determine the standard form of ${}F$.

Create a solution