What is Bases: Definition and 293 Discussions

The Business Association of Stanford Entrepreneurial Students (BASES) is a student group at Stanford University focusing on business and entrepreneurial activities. One of the largest student-run entrepreneurship organizations in the world, BASES' mission is to promote entrepreneurship education at Stanford University and to empower student entrepreneurs by bringing together the worlds of entrepreneurship, academia, and industry. BASES organizes the flagship 150K Challenge, Entrepreneurial Thought Leaders' Seminar, the SVI Hackspace, E-Bootcamp, and the Freshman Battalion.BASES was founded in 1996 by a group of five Stanford engineers. The organization works in partnership with Silicon Valley's venture capitalists and law firms to provide a variety of entrepreneurial services to Stanford students.

View More On Wikipedia.org
Recent contents Top users
  1. I

    Understanding Tensor Bases: Solving Equations in General Relativity

    I found this discussion online: http://web.mit.edu/edbert/GR/gr1.pdf The author tell me to verify that eq. (18) follows from (13) and (17). I'm not getting how that works on the basis of what he's given me so far. Take, for example the first expression. \textbf{g}=g_{\mu...
  2. L

    Changing the bases of logs question

    Homework Statement If x= log2aa y= log3a2a z= log4a3a prove that xyz +1 = 2yz Homework Equations loga C = log10C/log10a The Attempt at a Solution log= log10 x= log2aa = log a/ log2a y= log3a2a = log...
  3. D

    MHB Repeating decimals (sic) in bases other than 10

    Prove that $.0222\ldots$ (base 3) $= .1$ (base 3) $= \frac{1}{3}$ (base 10).First, we will show $.0222\ldots$ (base 3) $= \frac{1}{3}$ (base 10). \begin{alignat*}{3} 2\left(\frac{1}{3^2} + \frac{1}{3^3} + \frac{1}{3^4} + \cdots\right) & = & 2\sum_{n = 2}^{\infty}\left(\frac{1}{3}\right)^n\\ & =...
  4. M

    Separation using acids and bases

    I am doing a lab this week where the objective is to use acids and bases and a microscale extraction to separate three solids in a mixture. The mixture in question is a mixture of naphthalene, benzoic acid, and ethyl 4-aminobenzoate. It will then be put through a series of solvents and...
  5. P

    Find a transition matrix from bases?

    Homework Statement I have 2 bases, a = {1, x, x^2} and b = {-2 - 2x + 3x^2 , 1 + 2x - x^2 , -1 - x + 2x^2} of P2. Find the transition matrix Pab. How is this done?? Homework Equations Since this is Linear Algebra, there aren't really any relevant "Equations" as such. More logic...
  6. P

    Find a transition matrix from bases problem

    Homework Statement I have 2 bases, a = {1, x, x^2} and b = {-2 - 2x + 3x^2 , 1 + 2x - x^2 , -1 - x + 2x^2} of P2. Find the transition matrix Pab. How is this done??Homework Equations Since this is Linear Algebra, there aren't really any relevant "Equations" as such. More logic based...
  7. TrickyDicky

    Some doubts concerning the mathematical bases of GR

    I'm a little confused about certain assumptions usually made in GR as to how rigorous they are mathematically speaking. For instance the assumption generally presented without proof that GR spacetime manifold is a Hausdorff space seems not to be warranted given the fact that pseudometric spaces...
  8. P

    Adding in different bases proof

    Homework Statement Given that b>1,b\in\mathbb{Z},c_{0},c_{1},...,c_{m}\in\{0,...,b-1\}, 0\leq c_{m+1}\leq b-1, and c_{m+1}b^{m+1}=(\sum\limits _{k=0}^{m+1}c_{k}b^{k})\text{mod }b^{m+2}-c_{0}-c_{1}b-c_{2}b^{2}-...-c_{m}b^{m}, show that c_{m+1}\in\mathbb{Z}. Also, \sum\limits...
  9. D

    Operations on a State in Different Bases

    Say we have the same state \boldsymbol{\psi_r} in momentum basis, or \boldsymbol{\phi_p} in position basis. I want to make either a position observation or a momentum observation. How do I write the operation and the result mathematically, \mathbf{r} \boldsymbol{\psi}, \mathbf{r}...
  10. A

    Question about representation of numbers in different bases

    I'm thinking of expanding the numerical value of a real number in different bases. I want you guys to ensure some things for me so I know I'm not wrong. If X is the representation of a in the base B and Y is the representation of b in the same base(radix), can we say that X+Y = a+b? In...
  11. A

    Exploring Orthogonality: Combining Bases from Subspaces in Linear Algebra

    Hi: I have a problem about combine bases from subspaces. This is part of orthogonality. The examples as following: For A=##\begin{bmatrix} 1 & 2 \\ 3 & 6 \end{bmatrix}## split x= ##\begin{bmatrix} 4 \\ 3 \end{bmatrix}## into ##x_r##+##x_n##=##\begin{bmatrix} 2 \\ 4...
  12. S

    Bases of a Linear transformation (Kernel, Image and Union ?

    Bases of a Linear transformation (Kernel, Image and Union ? http://dl.dropbox.com/u/33103477/1linear%20tran.png For the kernel/null space \begin{bmatrix} 3 & 1 & 2 & -1\\ 2 & 4 & 1 & -1 \end{bmatrix} = [0]_v Row reducing I get \begin{bmatrix} 1 & 0 & \frac{7}{9} & \frac{-2}{9}\\ 0 & 1...
  13. D

    Find the bases for the eigenspaces of the matrix

    Homework Statement Find the bases for the eigen spaces? I handwrote the question and my work so it would be easier to read and attached it so see attachment. Homework Equations The Attempt at a Solution My work is on the attachment. My question is this what do I do when I have 3...
  14. W

    Can Ordinary Telescopes Detect Moon Bases?

    There is a lot of crazy conspiracy chatter, if its true, then what type of equipment do I need to see the moon bases or Mars bases? Thank you. I'm a real human, curious son of a b.
  15. S

    Constructing bases (worked out, please check )

    http://dl.dropbox.com/u/33103477/Union.png Omiting zeroes because they add nothing: \begin{bmatrix} 3 & 1 & 7 & 4\\ 5 & 6 & 7 & 3 \end{bmatrix} RREF \begin{bmatrix} 1 & 0 & \frac{35}{13} & \frac{21}{13}\\ 0 & 1 & \frac{-14}{13}& \frac{-11}{13} \end{bmatrix} Hence the basis is...
  16. Math Amateur

    Linear Transformations and Bases

    I need some help or at least some assurance that my thinking on linear transformations and their matrix representations is correct. I assume when we specify a linear transformation eg F(x,y, z) = (3x +y, y+z, 2x-3z) for example, that this is specified by its action on the variables and is not...
  17. K

    Acids and Bases calculation problems

    Homework Statement Data for Question B: (initial)[CH3COOH] = 0.500 mol dm–3 and) eqm [CH3COOH] = 0.200 mol dm–3; (initial)[CH3COO–] = 0.300 mol dm–3 and) eqm [CH3COO–] = 0.300 mol dm–3; The Attempt at a Solution Question A) " FInd the pH of a mixture of 50.0 cm3 of 0.100 mol...
  18. R

    Acids and Bases. How to tell if a compound is an acid or base or neautral?

    I've been given a question on how to tell whether a compound is an acid or base or neautral in an aquesous solution. Na2CO3 Please help.
  19. P

    Maximal number of bases for which composite number is Fermat pseudoprime

    According to the Wikipedia article a composite number n is a strong pseudoprime to at most one quarter of all bases below n . Do Fermat pseudoprimes have some similar property ? Is it known what is the largest number of bases for which composite n , that is not Carmichael number is...
  20. G

    2nd order ODE solution bases /wronskain question

    hello this question from my coarse notes has been giving me some trouble so i thought i would ask for some help on here, http://img88.imageshack.us/img88/9764/asfar.jpg i understand that since the bases are bases of the same solutions then they are just a multiple of each other, but...
  21. N

    Vectors: linear transformation and bases question

    Homework Statement Homework Equations The Attempt at a Solution i have answered the first part, explained why its a basis i think that i need to show that the N(T) = V alongside R(T) = W will give matrices that cannot be multiplied therefore T is the one that can't exist not sure...
  22. F

    Integral bases and Discriminants

    Here is my solution, I think I have part i) done OK, but I'm not sure about how to proceed with part ii). I suppose I need to show that both determinants of the base change matrices Cij and Dij are = ±1?Thanks
  23. C

    Do Dissolved Bases Form Ion Pairs in Water?

    I was told that when a base is dissolved in water, the ions form ion pairs so it is difficult to separate them completely; is this true? And if so, why wouldn't this apply to acids?
  24. S

    Converting between bases without base 10 mid-step

    I am currently trying to go between any two bases which are between and including base 2 to base 10. (i.e, base 10 to base 3, base 4 to base 6, etc...). Is there an equation or set of formulas for a one-step transition between the bases (or one-way method, rather than converting to base-10 then...
  25. T

    What is the proof that x, x^2, x^3 form a basis of V?

    Homework Statement http://img856.imageshack.us/img856/5586/screenshot20120121at328.png The Attempt at a Solution I propose the vectors x,x^2,x^3 form a basis of V. To test for linear independence, let 0 = a_1 x + a_2 x^2 + a_3 x^3, where a \in R. A polynomial is 0 iff all of its...
  26. W

    Simple question about vector spaces and bases in QM

    When reading in Griffiths and on Wikipedia about the vector space formulation of wavefunctions, i am constantly faced with the statement that a vector can be expressed in different bases, but that it's still the same vector. However, I'm having a hard time imagining what it is about a vector...
  27. S

    Difference among types of bases.

    Hello everyone, I am currently learning about bases, and I am confused about different types of bases. I understand how to obtain a basis for the null space of A or a basis for the range of A. I recently ran into a problem that simply asked me to find a basis for A. What does this mean? Does...
  28. S

    What is the approach for showing linear independence in a basis?

    1. Homework Statement See Attachment. Help with b) c) will be appreciated. 3. The Attempt at a Solution For the third question, my approach is sub in values for a and b which correspond to the co-effs. of the given basis. Then assemble a matrix from them. Eg...
  29. A

    Bases of linearly isomorphic vector spaces

    Finite-dimensional V and W are linearly isomorphic vector spaces over a field. Prove that if \{v_{1},...,v_{n}\} is a basis for V, \{T(v_{1}),...,T(v_{n})\} is a basis for W. My attempt at a proof: Let T:V\rightarrow W be an isomorphism and \{v_{1},...,v_{n}\} be a basis for V. Since T is an...
  30. S

    Proving a Basis for a Vector Space: A Step-by-Step Guide

    Homework Statement See Attachment. The Attempt at a Solution For the first two questions, I know I have to sub in values for a and b. But, I'm not sure what the output matrix is. The 3rd q, to prove B is Basis for R^3. I just have to row reduce [(1,5);(1,6)] to get [(1,0);(0,1)] right...
  31. S

    Bases, Subspaces, Orthogonal Complements and More to Come

    Homework Statement Show that the set W consisting of all vectors in R4 that are orthogonal to both X and Y is a subspace of R4. Here X and Y are vectors such that X = (1001) and Y = (1010). Part b) Find a basis for W. The Attempt at a Solution So I know to satisfy being a...
  32. S

    Splitting apart bases with a power

    Say I have (a+b+c)^n and I want to split it apart into a^something + b^something + c^something. Is this easily done?
  33. C

    Detection of Amino Acids and Nucleotide bases

    1. I need to detect amino acids and nucleotide bases that MAY be present in small quantities on Titan in the Hydrocarbon seas Homework Equations Not required this is for a mission analysis class The Attempt at a Solution So I'm working on a project for my fourth year class in...
  34. C

    Astrobiochemistry: Detection of Amino acids and nucleotide bases

    So I'm working on a project for my fourth year class in Space Mission Design and Analysis (I'm a fourth year space systems engineering student). My project is an astrobiology mission to Titan, Saturn's sixth moon, which is only slightly smaller than Mars with a atmosphere of Nitrogen of...
  35. C

    Nucleophiles vs Bases: Understanding Strong/Weak Reactions

    I am going through Sn1, E1, Sn2, E2 reactions and I'm trying to figure out if the reaction involves a nucleophile (strong/weak) or a base (strong/weak). I understand that you can differentiate nucleophiles and bases by their pKa value but that doesn't quite help me out, since I'm not given...
  36. T

    Bases for Vector Space V=\mathbb{R}^3

    Homework Statement Which of the following sets S are bases for the vector space V=\mathbb{R}^3? (a) S=\left\{ \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix} , \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} , \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \right\} (b) S=\left\{ \begin{bmatrix} 1 \\ 1...
  37. E

    Representing the state of a quantum system in different bases

    I am reading the book Introduction to Quantum Mechanics by David Griffiths and have come to the section on Dirac notation. It explains that the state of a quantum system is represented by a vector |β(t)> living out in Hilbert space, and, as with any vector, is independent of the choice of basis...
  38. K

    This guy is stealing my bases

    This guy is stealing my bases! nvm delete this please i got it
  39. M

    Finding the Matrix Relative to Basis B

    Homework Statement Let T be the linear transformation T=[1, 3, 2, 6] (the matrix has 1 and 3 on the top row and 2 and 6 on the bottom row) relative to the standard basis Find the matrix relative to the basis B= {(1, 2), (-3, 1)} Homework Equations The Attempt at a Solution So what I did was...
  40. K

    Ratio of logarithms in various bases to other bases

    I'm unsure as to if I am using the correct terminology, but what I mean by this is log = logarithm in base 10. ln = logarithm in base e. logx = logarithm in base x. Upon some investigation, I found that log(a)/ln(a)=log(b)/ln(b) where a and b are constants, meaning that there is a ratio...
  41. F

    Is bases the same as basis ? (Simplex Algorithm)

    Homework Statement [PLAIN]http://img193.imageshack.us/img193/3662/unledmcg.png The Attempt at a Solution I rewrote the whole thing in dictionary x_3 = 15 - 8x_1 - 4x_2 x_4 = 7 - 2x_1 - 6x_2 z = 0 + 22x_1 - 12x_2 x_i \geq 0 1\leq i \leq 4 a) So my basis/bases is x...
  42. D

    Why can the mixing of acids and bases be dangerous

    I tried googling this topic and basically all I could find was sites saying they neutralise each other - I know that. But why is it that when you mix say a drop of pH 14 solution with a lot of pH 1 solution that they react rather violently and the acid sprays everywhere? If someone could maybe...
  43. D

    Diagonal bases in transformations

    Homework Statement Let T: R3 - R3 be the linear operator given by T = -y + z -x + z x + y Find a basis B' for R3 relative to which the matrix for T is diagonal using the standard basis B for R3. Homework Equations [T]B' = P-1[T]BP The Attempt at a Solution...
  44. P

    Why Do My Amphoteric Equations Keep Going Wrong?

    Homework Statement I'm having problems understanding amphoteric acids and bases. I know amphoteric means that it can act as an acid or base, but when the question asks me to write the equation to support this statement, I always get it wrong :confused: Homework Equations HSO4^-1 is an...
  45. P

    Solving a log equation with (3) different bases

    I used to think I was master of any high school math course until I came across this log equation in a calculus textbook. \log_{2}x + \log_{5}(2x+1) = \ln x I use the change of base to convert everything to one base and then I get down to: (2x+1)^{\ln2} = x^{\ln2\ln5 - \ln5} I have no...
  46. G

    Salts and acids/ bases conceptual question

    My book says the following: NH4NO3 is weakly acidic as a salt because it is composed of the conjugates of the base NH3 and the strong acid HNO3. Why does that make it weakly acidic exactly?? Is it because the HNO3 is a strong acid, therefore it won't steal the protons that are...
  47. P

    Confused about the concepts of dual spaces, dual bases, reflexivity and annihilators

    My background in linear algebra is pretty basic: high school math and a first year course about matrix math. Now I'm reading a book about finite-dimensional vector spaces and there are a few concepts that are just absolutely bewildering to me: dual spaces, dual bases, reflexivity and...
  48. Rasalhague

    Topological and neighbourhood bases

    I'm trying to follow a proof in this video, #20 in the ThoughtSpaceZero topology series. I get the first part, but have a problem with second part, which begins at 8:16. Let there by a topological space (X,T). Let x denote an arbitrary element of X. Definition 1. Topological base. A set B...
  49. A

    Nonlinear Orthonormal Bases for Dynamical Systems in 3D

    I propose 27 scalar functions {fn : n = 1,2,…,27}, 9 delay-coupled 3D unit vectors {eij : i,j = 1,2,3} of general periodic nature, 7 ortho-normal bases {Zk : k = 0,1,2,…,6} each having three 3D unit vectors, 4 tensors {Y3,Y4,Y5,Y6} of order 2 and a tensor E of order 3. Z3-Z6 and E are defined...
  50. M

    Question relating to homogeneous system, subspaces and bases.

    Homework Statement Let A be an m x n matrix such that the homogeneous system Ax=0 has only the trivial solution. a. Does it follow that every system Ax=b is consistent? b. Does it follow that every consistent system Ax=b has a unique solution? The Attempt at a Solution So if the homogeneous...
Back
Top