1. M

    complement and supplement identities problem

    Hi everyone. I need help on the following problem: (1/sinx)-(1/tanx) = tan(x/2), where x is in degrees. How do you reduce the "left hand side" to the "right hand side" using trigonometric identities? Thank you.
  2. L

    a schur complement application

    Dear all, I have a question about the Schur Complement. Is the following inequality $\left[ {\begin{array}{*{20}{c}} {{A^T}P + {K^T}{B^T}P + PA + PBK + C_z^T{C_z}}&{P{B_w}} \\ {B_w^TP}&{ - \gamma } \end{array}} \right] \prec 0$ equivalent to $\left[ {\begin{array}{*{20}{c}} {{A^T}P...
  3. G

    complement and null space

    if A is a submodule of M, M = R^n, the null space of Q is defined as {x|Qx = 0} where Q is n by n matrix with entries in M. The complement of A is B so M = A+B( inner direct sum). I am trying to prove that if A has a complement in M, so A is the null space of Q for some Q( n by n matrix with...
  4. D

    Diminished Radix Complement (geometric pattern)

    So I'm reading about Radix Complements on Wikipedia, and there is a geometric pattern used to prove the following statement: The radix complement is most easily obtained by adding 1 to the diminished radix complement, which is (bn-1)-y. Since bn-1 is the digit b-1 repeated n times because bn-1...
  5. J

    orthogonal complement

    Let $\{w_1,w_2,...,w_k\}$ be a basis for a subspace$W$ of $V$. Show that $W^{\bot}$ consists of all vectors in $V$ that are orthogonal to every basis vector. I know that the intersection of the two subspaces is a set containing only the zero vector. the set is a basis so it's linearly...
  6. X

    Probability with Complements

    Hi, I'm confused as to how to find probabilities with complements. The question is: Let P(A) = 0.4, P(B) = 0.5 and P(A intersect B) = 0.3 What is? P(A intersect B') <---(That is B complement) P(A' intersect B') <---(A complement intersect B complement). For, P(A intersect B'), I have...
  7. N

    Complement graph not planar

    Hello, I have the following question: Let G be a simple graph with 2 connected components. Each component has at least 3 edges. Prove that G's complement graph is not planar. Now what I thought would make sense is that all the edges in the complement graph cross each other so it can't be...
  8. S

    Graph or complement contains complete graph

    I am trying to prove that given any graph G on 4^n vertices, either G or its complement contains K_n (the complete graph on n vertices) as a subgraph. I am tutoring students who have not had any graph theory, and they are supposed to approach the problem combinatorially (supposedly just applying...
  9. D

    What is the complement of this set

    (interval, actually) [a, \infty ) I see the complement contains at least the interval (-\infty ,a). Anything else? I want to say no. Thanks!
  10. L

    Using DeMorgan's Law, write an expression for the complement of F

    Using DeMorgan's Law, write an expression for the complement of F if F(x,y,z)= xy + x'z + yz' I know this property: (x'y') = (x' + y') and (x' + y') = x'y' But there's only one variable that is NOT'ed at a time, (x in the x'z and y in yz').
  11. D

    Definition of Complement

    I'm having trouble understanding the following: Does Ec mean that all events in the sample space (besides E) necessarily happen, or simply that E does not happen? In other words, if the sample space is S={A,B,C,D,E} does Ec imply A,B,C, and D have occurred, or just that E hasn't occurred?
  12. O

    Kernel is orthogonal complement

    Let L:Rn -> Rm be linear transformation with matrix A. Show that ker(L) is orthogonal complement of row space of A.
  13. T

    orthogonal complement

    W is the subspace of R^{4} with basis { w1 , w2, w3} where w1 = (1 ,1 ,3,2) w2=(1,1,-2,-3), w3=(2,1,-3,-1) Find the orthogonal complement of W is R^{4} Am not sure how to find it, do i multiply w1*w2*w2 = 0 ?
  14. F

    2's complement conversion

    Hello, can someone please tell me if I am on the right track with these please. Find the integer value (i.e. negative number) of the binary number using 2's complement: binary / uinsigned integer / 2's compement integer value 0111 1111 1111 1110 / 32766 = 32766 0111 1111 1111...
  15. J

    Schur complement proof

    Trying to prove that if A > 0, then $M$ is positive semidefinite if and only if $C=B^*$ and $D-CA^{-1}B \ge 0$ I have written M=\begin{pmatrix} A&B\\B^*&D \end{pmatrix}= \begin{pmatrix} 1&BD^{-1}\\0&1 \end{pmatrix}\begin{pmatrix} A-BD^{-1}B^*&0\\0&D \end{pmatrix}\begin{pmatrix} 1&BD^{-1}\\0&1...
  16. M

    Finding Orthogonal Complement

    Hi! So I'm not totally sure what to do here... so if p(x)=x and W = span{p} what is W⊥ ? I thought I would use {1,x} as a basis and then u1 = 1 u2 = 1 - proju1(v2) so then u2 = 1 - (<1,x>/<1,1>)*1 That didn't really seem to come out right though. can anyone help me?
  17. M

    Complement of nonempty open set

    I've tried to think this, help would be appreciated to get me going a gain. If we have two nonempty open set A,B \subset {R}^{n} so that A \cap B = \emptyset (two separate sets). How could I show that complement of union A and B is also nonempty, \complement (A \cup B) \neq \emptyset. I'm...
  18. L

    Clarification on some set notation

    I have a homework problem that reads as (A symmetric difference B) with a line over the top. (This is just part of the problem - I'm trying to be sure I'm not asking for the answer, just clarifying the bits I don't understand.) Does that mean the complement of the symmetric difference as a...
  19. M

    Complement of a subgroup

    Let G be a finite group. Suppose that every element of order 2 of G has a complement in G, then G has no element of order 4. Proof. Let x be an element of G of order 4. By hypothesis, G=\langle x^{2} \rangle K and \langle x^{2} \rangle \cap K=1 for some subgroup K of G. Since [G:K]=2, then K is...
  20. S

    Schur Complement Problem (Spectral/Num. Lin./Matrix Theory)

    Let $A \in F^{n \times n}$ be written in block form $A = \begin{pmatrix} A_{1,1} & A_{1,2} \\ A_{2,1} & A_{2,2} \end{pmatrix}$ where $A_{1,1} \in F^{k \times k}, A_{1,2} \in F^{n \times (n-k)}, A_{2,1} \in F^{(n-k) \times k}, A_{2,2} \in F^{(n-k) \times (n-k)}$. Let $S =...