1. L

    A knotty outcome in space

    Consider a finite string, floating in space, of diameter negligible to its length. Will it eventually become permanently knotted due to randomness?
  2. M

    Move 2d polygon in 3d space onto 2d plane

    I have a series of 3d points in space they are on an arbitrary plane but i want to move them to a plane AX+BY+CZ+D=0 A=0, B=0, C=1, D=0 so the XY Plane. the matrices for this is identity. From the points i assume 0) All vectors will be unitized 1) the first point in the polygon will...
  3. C

    Sample Space Question (Algebra 2) [Probability]

    Hey everyone, I needed help solving this problem for an assignment, I literally have no clue how to solve it. It's worth 10 points so it would mean a lot if someone could help. Thanks!
  4. S

    Quotient space

    If W is a subspace of a vector space V over the field (Z3) Integer modulo 3 such that Dim(V)=7 and Dim(W)=4, then the number of element in V/W is how much? I can only deduce that number of elements in the basis of V/W will be 3. How to find the total number of elements in V/W?
  5. W

    Plane in three-dimensional space

    Determine an equation of the plane whose points are equidistant from (2, -1, 1) and (3, 1, 5). -- Answer: x + 2y + 4z = 29/2
  6. P

    Boiling and Melting point of Liquids in space. Do the Boiling and Melting point of Liquids vary in Space? Thanks & Regards, Prashant S Akerkar
  7. P

    Why are things squared in formulas about light, space etc.

    As a beginning math student I've wondered: why is the square prominent in math formulas about the natural world, instead of the circle? Circular light beams, elliptical solar systems and galaxies, Inverse Square Law, seem to me better defined in terms of the circle than squares, which don't...
  8. S

    proving null space

    Hello, given A is NXN matrix I need to proof or disprove the following:
  9. W

    Convergence in a normed vector space - Linear operator

    Having X a normed vector space. If f is a linear operator from X to ℝ and is not continuous in 0 (element of X) , how can we show that there exists a sequence xn that converges to 0 for which we have f(xn) = 1 (for all n element of ℕ). Any help would be greatly appreciated, thank you.
  10. W

    Adherence of subset - Kernel

    Having Y, a subspace of X. How can we show that the adherence of Y can be expressed as : Adherence of Y = intersection of { Ker(f) | f element of X* , Y contained in Ker(f)}
  11. L

    basis for left null space

    How can we find the basis for left null space? specifically for these matrices A( 1 2 5 and B=(1 2 5 2 7 10 ) 2 4 10) what I did was : A transpose 1 2 2 7 5 10 reduced...
  12. L

    Data structure for finding max, inserting and deleting in O(1) and O(n) space

    This is an interview question. I needed to implement a data structure that supports the following operations: 1. Insertion of an integer - $O(1)$ 2. Deletion of an integer (If for example we call delete(7) so 7 is deleted from the data structure, if the...
  13. V

    Orthonormal basis B:{e1,e2,e3} with respect to an inner product space

    We have the inner product <(x_1,x_2,x_3),(y_1,y_2,y_3)>=3x_1y_1+x_1y_3+y_1x_3+x_2y_2+2x_3y_3 I'm asked to find the orthonormal basis of R^3 that is given from the normal basis B=(e_1,e_2,e_3), e_1=(1,0,0), e_2=(0,1,0), e_3=(0,0,1) with respect to the above inner product I guess I should...
  14. L

    Question - Sample space in probability

    I would like to know how to solve the following question: Throw a cube until you get the number 6, then stop throwing. a) What is the sample space of the experiment? b) Let's call the event to throw the cube n times En. How much points from the sample space are within En?
  15. L

    Fill D space with D-1 object?

    Is there a finite object of dimension D-1 that can fill a space of dimension D?
  16. Z

    Isotropic Space

    Prove: 1. Any max isotropic space has dim n 2. Let f be a non-generative symplectic and I is a subspace of V be a max isotropic space. Prove that there exists an isotropic space I' such that V=I+I' 3. Let f be a symmetric form on C$^2$$^n$. Prove that both results above hold
  17. H

    How to combine 2 angles in 3D space

    Hi folks, I have a bit of a problem and I can't seem to picture it in my mind or think of a way to draw it to help me solve it. I'm working in a editing/compositing piece of kit called Flame. In a 3D environment there is a camera which acts as the point of view and a flat finite surface...
  18. B

    Proving a distance of a metric space

    Let be in an Euclidean metric space ($\mathbb{R}^2$). Is the distance $d(x,y)=(x-y)^2$ a distance? I have to prove it or not. My problem is the triangle inequality, I don't find any tool to use! $$d(x,y) \le d(x,z) + d(z,y) \longrightarrow (x-y)^2 \le (x-z)^2 +(z-y)^2$$. Can you...
  19. P

    How to calculate the Sample Space S

    Hi, I'm currently studying up on the basics of probability. One thing that keeps eluding me is how to properly calculate the sample space. From the examples I have seen, they have visually done this. However, this is, of course, not possible or practical if one wants to create formulas or...
  20. M

    properties of inner product space

    hello everyone! i am having a question and a problem regarding the properties of an inner product space. the question is: if a= \begin{pmatrix}4&1\\ 1&5\end{pmatrix}. then if we say v=(y1,y2),u=(x1,x2), the inner product in the standart base based on A would be (u,v)=4x1y1+x1y2+x2y1+5x2y2...