As definition, in order to find the isotropic points of a jacobian matrix, the matrix's columns become orthogonal and equal to the magnitude. I don't quite understand this definition. if i have a matrix looks like this:
a b
c d
Matrix example:
2.x 0
2.y+3 3
How can I find its isotropic points ?
Thank you very much.
The columns must be orthogonal to each other (i.e., the dot product of any two columns must be equal to $0$), and their vector norms must be equal. For the general $2\times 2$ matrix $$ \begin{pmatrix} a & b \\ c & d \end{pmatrix} $$ these requirements amount to: $ab+cd=0$, $a^2+c^2=b^2+d^2$.
For the concrete example $$ \begin{pmatrix} 2x & 0 \\ 2y+3 & 3 \end{pmatrix} $$ the above requirements simplify to $2y+3=0$; $(2x)^2+(2y+3)^2 = 9$. Hence $y=-3/2$ and $x=\pm 3/2$.
