Solve \(\displaystyle{x}^{{{T}}}{A}{x}={k}\) with \(\displaystyle{k}={c}{t}{e}\)?

meli199939f

meli199939f

Answered question

2022-03-21

Solve xTAx=k with k=cte?

Answer & Explanation

cineworld93uowb

cineworld93uowb

Beginner2022-03-22Added 16 answers

Step 1
After diagonalization of the matrix (which is a rotation of the basis), the equation becomes
λu2+μv2+νw2=1,
which is the equation of an ellipsoid, as λ,μ,ν>0. (If you make w constant, i.e. cut with a plane, you should recognize the equation of an ellipse.)

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