how do I plot this surfaces in 2-D?

Let $x_1$ and $x_2$ be two real numbers and define the column vector $\mathbf{x}=[x_1,x_2]$. Let $\mathbf{A}_1$ and $\mathbf{A}_2$ be two $2\times 2$ real symmetric matrices. Then I need to plot the surfaces \begin{align} \mathbf{x}^T\mathbf{A}_1\mathbf{x}+1 &\leq 0 \\ \mathbf{x}^T\mathbf{A}_2\mathbf{x}+1 &\leq 0 \end{align}

How do I do this in Mathematica?

• Please try to write some code. Aug 11, 2014 at 4:13
• @belisarius I really want to and I understand it is inappropriate to ask without trying. I come from a matlab & engineering background and doing this in matlab is a pain. Just started with mathematica 2 hrs back. Aug 11, 2014 at 5:32
• Well, you've a kickstart below Aug 11, 2014 at 16:51

SeedRandom[84];
a = # + Transpose@# &@RandomReal[{0, 1}, {2, 2}];
RegionPlot[{x, y}.a.{x, y} > 0, {x, -2, 2}, {y, -2, 2}]


• +1, but the condition is $x^TAx+1\le0$, not $x^TAx>0$.
– user484
Aug 11, 2014 at 6:33
• @RahulNarain Nobody is perfect :) Aug 11, 2014 at 7:07

Using V10 functionality and borrowing from Belisarius:

SeedRandom[84]
a = # + Transpose@# &@RandomReal[{0, 1}, {2, 2}];


We create an ImplicitRegion

region = ImplicitRegion[First[{x, y}.a.{{x}, {y}}] > 0, {x, y}];


And discretize it:

DiscretizeRegion[region, {{-2, 2}, {-2, 2}}]


If you want Frame:

Show[%, PlotRange -> {{-2, 2}, {-2, 2}}, Frame -> True]