# Search results

1. ### I Meaning of Third Eigenvalue in a Tilted Ellipse in a 3x3 Matrix

I think you'd be right if my vector, x, was (x, y, z), but it's (x, y, 1). I was doing that to account for 2bx and a 2dy terms (whereas the 2 x 2 only has x^2, y^2, and xy terms). Perhaps this step isn't valid, but without my choice of this vector, I don't know how you'd model something like...
2. ### I Meaning of Third Eigenvalue in a Tilted Ellipse in a 3x3 Matrix

While reading the Strang textbook on tilted ellipses in the form of ax^2+2bxy +cy^2=1, I got to thinking about ellipses of the form ax^2 + 2bx + 2cxy + 2dy + ey^2=1 and wondered if I could model them through 3x3 symmetric matrices. I think I figured out something that worked for xT A x, where x...
3. ### Confused about the True Geometric Meaning of a Dot Product Answer.

Okay, so thinking about your response leads me to another question. Let's take the example you provided (W=Fd) and the dot product I mentioned. Let's say that F= (1,4) and d= (5,0). Am I correct in saying that this dot product would imply a force of 1N acting for 5m, and another of 4N acting...
4. ### Confused about the True Geometric Meaning of a Dot Product Answer.

I have performed numerous calculations of dot products throughout my math courses, but I think I lack a fundamental understanding of what it actually means, beyond the abstract way I have been taught to deal with them. I know the definitions (it's the inner product, or the projection of A on to...