0
votes
0answers
31 views

Testing if a n-dimensional ellipsoid lies completely in an n-dimensional cuboid

I have a n-dimensional ellipsoid A and a n-dimensional cuboid B. I need to know if A lies completely in B. How can I test whether this condition holds? Even better would be a solution telling what ...
1
vote
2answers
65 views

What is the mathematical term that can differentiate two same vectors?

Say i have two vectors A and B. Mathematically they are same if they have same magnitude and direction. So, say if someone asks me to draw a "vector" of 5 magnitude with 45 degree angle with ...
0
votes
1answer
87 views

Lines which intersect the postive half axis of x

We have to find out which lines intersect the postive half axis of x. According to this formula we can determine if the angle between two points(A[x1,y1] and B[x2,y2]) of the line (angle A0B where 0 ...
0
votes
1answer
73 views

a certain set of polynomials forming a subspace

Just out of curiosity: Why is it that all polynomials vanishing on an irreducible component in some affine space form a vector subspace? Thanks for your time.
2
votes
0answers
103 views

Is the notion of a dual space related to the set of polynomial functions on an affine algebraic variety?

Let $M$ be an affine algebraic variety and consider the ring of polynomial functions on $M$, $\mathcal{O}(M):=\{f: M\to k : f\text{ a polynomial}\}$. If $k$ is algebraically closed we can recover our ...
0
votes
1answer
114 views

Show that (vector) subspaces of $\mathbb{A}^n$ are algebraic sets

i have just started to learn some algebraic geometry and there is a statement in the notes i am following that i do not understand: "Subvector spaces of $\mathbb{A}^n$ are algebraic sets. They are of ...