Recent content by Zaphos

The augmented matrix is just a different notation for writing a matrix equation like Ax=b -- smoosh A and b together, and you have the augmented matrix representing Ax=b. This notation is convenient for algorithms like Gaussian elimination, but conceptually I find it nicer to look at the...

Maybe it'll be more clear to look at the non-augmented system first \begin{pmatrix} x_1^{2} & x_1 & 1 \\ x_2^{2} & x_2 & 1 \\ x_3^{2} & x_3 & 1 \end{pmatrix} \begin{pmatrix} a\\ b\\ c\\ \end{pmatrix} = \begin{pmatrix} y_1 \\ y_2 \\ y_3 \end{pmatrix} Multiply out a row...

re the negative -- that equation is going to put a negative number in the square root whenever the line changes more in y than x? So, I'm guessing it's a typo and they mean + not - ...

No, I think you'd potentially need an infinite number of them for a bounded function as well, so that doesn't sound like a good explanation. Yes.

In addition to the two imaginary eigenvalues, the most intuitive one (for me) is the real valued one -- it's 1, with eigenvector along the axis of rotation. You can see that one just by noting that rotating won't change a vector along the axis of rotation. edit: Quaternions could be...

Unfortunately that fitting problem is a lot trickier ... With the height field method, your 'error' was 'distance in z from the point to the surface' which falls out quite naturally from the function f(x,y) = z. But when you have a surface implicitly defined by f(x,y,z) there is no...

The a8 = -1 is because a8 is the coefficient of z, and your original equation is f(x,y) = z while your plotting function's equation is f(x,y,z) = 0, so we need to subtract z from both sides of the original to get the equations to match up. That gives f(x,y) - z = 0, so the coefficient of z is...

The coefficient a8 should be -1. So you're subtracting z from both sides of your original equation. a9 should be f like you said.