Bases Definition and 294 Threads

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.

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  1. D

    Need general algorithm for finding dual bases

    hi, this is my first post on this site so please excuse me (and correct me) if i am not posting according to the guidelines. im studying right now linear transformations and I am a bit shaky concerning dual vector spaces. i understand the definition but am not sure how to apply it. what...
  2. M

    How to Find the Base in an Equations with Unknown Numbers

    How would you solve a problem like this where you have to find what base A is for this equation to be true? So in what base are these numbers.24)A + 17)A = 40)A Not asking the answer for this particular question but how you'd solve it (other than trial and error obviously)
  3. W

    Mixtures of Acids and Bases: What Type of Solution is Produced?

    Homework Statement You prepared a reaction table for 10.0 mL of 0.1 M NH4Cl with 5.0 mL of 0.1 M NaOH. Please choose all of the following that describe the solution that was produced. The choices are: 1. a solution containing only a strong base 2. a solution containing a weak acid and a...
  4. C

    Using indicators to determine acids, bases, and salts

    Hey, I just got out of my lab at school and just realized that me and my professor made a mistake. He marked my lab complete, and I also thought it was complete, however, I just realized that there was something missing. The problem is that I can't go back into the lab to try it out again...
  5. S

    Concentrations of conjugate bases at specific pH levels

    The pKa for the dissociation of H3PO4 is 2.15. What is the concentration of H2PO4-1 (in M) at pH 3.21 if the original concentration of the phosphate was 2.37 M? My Attempt: Key Information: pH final: 3.21 Initial Molarity of phosphate: 2.37 M pKa: 2.15 I started with the first...
  6. G

    Linear transformation between bases

    Hi ! I am a little bit confused with notation in the following: Let A= \begin{bmatrix} 2 & 3 & 4 \\ 8 & 5 & 1 \\ \end{bmatrix} and consider A as a linear transformation mapping \mathbb{R}^3 to \mathbb{R}^2. Find the matix representation of A with respect to the bases...
  7. J

    Exploring Acids & Bases: Sodium Acetate & Cyanide Solutions

    Here's the question: And the answer is: Which makes sense to me, because acetic acid is the stronger acid. But there's another option in the list that it says is NOT true: I thought this might be true, because both are solutions of chemicals that were referred to as acids. Am I...
  8. S

    Is it possible to determine if a number is a perfect square in different bases?

    Does anyone know if its possible to check whether a number is a perfect square in 2 different bases ? ( I don't mean the representation of a number in 2 different bases - coz that would be a ridiculous question , what I mean is consider a no say xyz - is it possible to prove / disprove that it...
  9. CarlB

    Spin and position and mutually unbiased bases

    If you measure the position of an elementary particle exactly, then its position becomes unknown. So consecutive measurements of position do not give the same result. There's been some recent papers by G. Svetlichny, J. Tolar, and G. Chadzitaskos that show that position measurements move around...
  10. J

    Easier Way to Simplify log_3 3x?

    hey guys, i have a question, then i will show my solution, is there any chance you guys could help me find an easier way to get to the answer, cheers question: log_3 3x answer: log_a (yx) = log_a (y) + log_a (x) log_3 (3) + log_3 (x) log_a (y) = x -> y = a^x -> log_a (a) = 1...
  11. P

    Linear transformation from given matrices - bases unknown

    Homework Statement Find a linear transformation T: P_2 \rightarrow M_{22} such that T(1+x)=\left[\begin{array}{cc}1&0\\0&0\end{array}\right] T(x+x^2)=\left[\begin{array}{cc}0&1\\1&0\end{array}\right] T(1+x^2)=\left[\begin{array}{cc}0&0\\0&1\end{array}\right] The Attempt...
  12. C

    F4 algorithm for calculating Groebner bases

    Dear all, I have a question concerning Faugere's improved F4 algorithm. You can find it in the attached file faugere_f4.pdf on page 9. In section 2.6 (page 14) an example is given for how the algorithm works. According to the example the second while-loop in the improved F4 algorithm...
  13. L

    Differentiating Acids and Bases Based on Chemical Formulas

    Homework Statement does anyone know how i can differentiate a strong acid from a weak acid and likewise for a strong base and a weak base based on its chemical formula? Homework Equations The Attempt at a Solution
  14. A

    Bases, Invertibility and Injectivity Query

    Hi There are two things that are confusing me a bit, and was wondering if anyone could explain them. Firstly, if we let V1,V2,...,Vn be vectors in some field F^n and let P = {V1,V2,...,Vn}, then the following are equivalent: (i) {V1,V2,...,Vn} is a basis for F^n ; (ii) P is...
  15. M

    Difference between vector basis and bases?

    Homework Statement Could someone please explain the difference? Maybe show some examples? Than you! Homework Equations The Attempt at a Solution
  16. S

    Unable to understand why bases in DNA which make V-A-P codon in bacter

    Homework Statement Which bases in DNA do make V-A-P codon in a bacter? The Attempt at a Solution I know that the right answer is C-T-G. However, I do not understand why. I know the base rules that the amino acid A wants T, and the amino acid C wants G. This does not explain the...
  17. S

    Struggling with Acids and Bases Concepts in Chemistry AP?

    I was looking for information in regard to Acids and Bases. I'm having a awful time with conceptual questions concerning this chapter in class, and I'm getting pretty frustrated. Any practice questions / supplemental in depth tutorials would be nice. Thanks!
  18. N

    Is the Scalar Product Invariant Under Coordinate Changes?

    Homework Statement Hi all. Lets say that we are looking at an operator Q, and two eigenstates given by |1> and |2>. The eigenstates |1> and |2> are not eigenstates of Q, but of some other operator H. My question: Is <1|Q|1>, <1|Q|2>, <2|Q|1> and <2|Q|2> independent of the basis used as long...
  19. K

    About bases of complex (Hilbert) space

    Hi there, In 3-dimensional real linear space, the simplest bases can be taken as the canonical bases \hat{x} = \left(\begin{matrix}1 \\ 0 \\ 0\end{matrix}\right), \qquad \hat{y} = \left(\begin{matrix}0 \\ 1 \\0\end{matrix}\right), \qquad \hat{z} = \left(\begin{matrix}0 \\ 0 \\...
  20. D

    Experimenting with Acids & Bases: DeltaH, Dissociation & Bond Strength

    I did an experiment with a) strong acid (HCl) and strong base (NaOH) b) weak acid (ethanoic) and strong base (NaOH) so, I am looking at the heat of energy for both the reactions, and so i found that reaction a had a greater heat of energy was that of the reaction b) weak acid and...
  21. D

    Bronsted - Lowry Theory Of Acids and Bases

    Homework Statement Some of the books I have state that the equation of... HCl + NH3 --> NH4+ + Cl- While others state that the above equation should be written as... HCl + NH3 --> NH4Cl Which one is correct? I think the answer should be the second one since the two compounds...
  22. E

    How do you change a base directly without using base 10 or base 2?

    Homework Statement How do you change a base into another number directly without changing to base 10 or base 2 for example? Eg changing 1442 base 6 to base 3 = 112022 Just want to know the steps in the division Teacher wants us to do it this way for less error Help appreciated
  23. Mentallic

    Exponents with different bases

    Homework Statement This is re-asking the question in https://www.physicsforums.com/showthread.php?t=273275" which mysteriously went quiet before the answer could be given... Anyway I also tried answering the question, but to no avail. Homework Equations a^m.a^n=a^{m+n} (a^m)^n=a^{mn}...
  24. X

    [Chemistry] questions on solubilty of bases and naphthalen-2-ol

    Homework Statement 2-hydroxybenzenediazonium ion is allowed to react with naphthalen-2-ol to form 1-(4-hydroxyphenylazo)-2-naphtholHomework Equations 1.Why is amine having a different solubility in water and dilute hydrochloric acid? 2.Why is naphthalen-2-ol dissolves in sodium hydroxide...
  25. W

    Which DNA and RNA bases contain a carbonyl group?W

    which DNA and RNA bases contain a carbonyl group? Which DNA and RNA bases are primary amines? Thanks for any help
  26. F

    Quantum state: how many bases?

    A single particle quantum state \Psi is given a by a wave function (vector) representable as a linear superposition of eigenvectors \Upsilon weighted by a number proportional to their probability of occurrence: \Psi=a_1 \Upsilon_1+a_2 \Upsilon_2+... In the case of the observable "spin"...
  27. N

    Is Every Subset a Subspace in Vector Spaces of Functions?

    Hi How can I work out which subset is a subspace and which one isn't on this problem: Fq ([0,1]) be vector space of all functions [0,1] -> Q with addition and scalar multiplication defined in usual way. Let U < Fq ([0,1]) be the subset consisting of all functions f s.t. f(0) >= f(1) and...
  28. K

    Linear Algebra question: finding bases

    Homework Statement The problem states: Let A_1 = [-1 1] , A_2 = [1 3] ...[0 1]...[-1 0] A_3 = [1 0] , A_4 = [0 -1] ...[1 2]...[2 3] Show that {A_1, A_2, A_3, A_4} is a basis for M_2 R. The attempt at a solution I'm very confused about this problem. I understand that to...
  29. F

    Linear Transformation with Respect to Given Bases

    Let T: R3 -> M(2,2) be the linear transformation given by T(x,y,z) = [ z ...-z ] .....[ 0 ... x-y]Fix bases B = {(1,0,0),(0,1,0),(0,0,1)} and C = { [1 0] , [0 1] , [0 0] , [0 0] } ............[0 0]...[0 0]...[1 0]...[0 1]for R3 and M(2,2) respectivelya) Find the matrix [T]c,b of T...
  30. E

    Number Theorems and Number Bases

    I am probably not phrasing this question precisely enough but ... ... are Number Theorems true regardless of the Number Base? In particular, is any given Number Theorem that is true in Base 10 equally true in Base 2? Thank you. Euan
  31. S

    Number theory, converting numbers too different bases

    Homework Statement Show that for any fixed a and b, there is an algorithm to convert an n-digit number from base a to base b with O(n^2) operations. The Attempt at a Solution Really i am completley lost here. Working backwards, i know to convert from base a to a base b you must use...
  32. H

    Exponents with different bases

    Homework Statement 4^(x+2)=9 Homework Equations basically all I want to know is what is the best way to go about solving a problem like this. The Attempt at a Solution I know how to convert a problem as such 4^(3x)=10 using. [log(<base>4,10)]/3 = X. however I need some help with...
  33. C

    Determining the Most Effective Buffer Solution for pH Stability

    Hi there I was wondering if anyone could help me with this buffers question ... For which of these liquids is the pH likely to change least if a splash of concentrated sulphuric acid is added? Justify your answer: a) 0.1M hydrochloric acid solution b) 0.08M ethanoic acid/0.02M potassium...
  34. K

    PKa values for weak/strong bases

    In chemistry it's normal to distinguish between weak and strong acids. Is there a limit for the pKa value that determines what is strong and what is weak? Equivalent, for bases, is there a pKb value that separates weak and strong bases?
  35. D

    How can one solve an equation with logarithms and powers of a base?

    In class, I had a question about how to solve the following problem: 6^log6_3 (EDIT: if this is ambiguous without the math formatting, (I don't know how to format it) it reads 6 to the power of log base 6 that yields 3) No one knew how to solve it (including the teacher), and he could...
  36. X

    Acids, Bases, and Salts: Essential Equations and Laws for Success in Class

    [SOLVED] Acids, Bases, and Salts I will be starting on a new chapter unit of Acids, Bases, and Salts for class. I was wondering what important information I should be aware of, like equations and laws since I want to stay ahead of my class, and not die if I miss a day.
  37. A

    Linear transformation with two given bases

    Homework Statement (a; b) is in terms of D = ( 1,1 ; 1 -1) and (c; d) is in terms of Dx = ( -1,1 ; 0,2), then we need to find a matrix such that (c;d) = (?, ?; ?, ?)* (a; b). Homework Equations y = Ax >> linear transformation The Attempt at a Solution I know the answer is [1, -3...
  38. A

    Chemistry - acids, bases, equilibrium

    Homework Statement Like all equilibrium constants, Kw varies somewhat with temperature. Given that Kw is 3.49e-13 at some temperature, compute the pH of a neutral aqueous solution at that temperature. Homework Equations Kw = [H+][OH-] pH = -log[H+] The Attempt at a Solution 3.49e-13 =...
  39. T

    A question on changing bases of numbers

    i want to transform a number in base 6 into a number in base 3 i was looking for a way to transform straight forward without any middle man ("from 6 to 10 and from 10 to 3" that's not the way i am looking for)
  40. N

    Finding the matrix with respect to two bases

    Homework Statement If I am giving a matrix A representing the linear transformation L(x) = Ax, then A is the matrix-representation of L with respect to the basis elements in the vector-space S (standard). If I am now given another vectorspace V by the matrix V, and I want to find the matrix B...
  41. N

    Vectors that form bases (linear algebra)

    [SOLVED] Vectors that form bases (linear algebra) Homework Statement I am given two vectors u and v, which are: u = (1/2 , 1/2 , 1/2 , 1/2) and v = (1/2 , 1/2 , -1/2 , -1/2). I have to find an orthonormal basis for R^4 containing u and v. The Attempt at a Solution The first thing...
  42. N

    Matrices with respect to two bases

    Homework Statement I have two questions: 1) When I am asked to find the matrix with respect to two bases E and F, that is NOT the same as finding the transition-matrix going from E to F? If not, what does that matrix (with respect to E and F) represent then? 2) If I have a vector-space which...
  43. N

    Linear algebra - finding bases

    Homework Statement I have three vectors F, G and H and I want to find the basis for R^5 that contains the three vectors F, G and H. The Attempt at a Solution I write the matrix A <F G H I>, where I is the 5x5 identitymatrix. I bring this matrix to rref, but which columns must I choose...
  44. N

    Linear algebra; changing bases

    [SOLVED] Linear algebra; changing bases Homework Statement I have two bases E and F given by: E = [1, x, x^2] F = [1-x, x-x^2, x^2]. I want to find the transition-matrix S that goes from E to F. The Attempt at a Solution To do this, I must write one basis as a linear combination...
  45. A

    Bijection between infinite bases of vector spaces

    I am reading "The linear algebra a beginning graduate student ought to know" by Golan, and I encountered a puzzling statement: Let V be a vector space (not necessarily finitely generated) over a field F. Prove that there exists a bijective function between any two bases of V. Hint: Use...
  46. H

    Solving Euler Cauchy Equation: Y1,Y2, X^2 & More

    If for example, I have. Y1=Cos(2Ln(x)) and Y2=Sin(2Ln(x)) and I have to reach the general solution. I know how to get to the general solution is the cauchy equation: y'' X^n + y' x + 4 y = 0 According to the answer, n=2 => y'' X^2 + y' x + 4 y = 0 How am I to know that that it is X^2 ? Or is...
  47. E

    Why is the infinite Cartesian product of [0,1] with itself not countably based?

    A question about bases I have a question as to why a particular space does not have a countable base. The space is the infinite Cartesian product of the interval [0,1] with the usual topology, with itself.
  48. E

    Topological Bases: Are Two Definitions Equivalent?

    Homework Statement I have seen two definitions for the topology generated by a basis set: one here http://books.google.com/books?id=9cT2wI-Qrk4C&pg=PA23&dq=basis+for+a+topology&ei=wu3nRua6HYqKoQLlj81v&sig=nNFNyWXorlwCQ8WCwQBDTuI9HUc#PPA22,M1 and the other one is a set U is open if for every...
  49. K

    Titration with Carbonates acting as bases

    Homework Statement when a carbonate acts as a base and neutralises an acid, CO2 is formed. the problem is that some of the CO2 dissolves in the water and forms Carbonic Acid.the Carbonic acid will affect the titre value as it will react with the base, along with the HCl. How do we prevent...
  50. R

    What is the matrix for T relative to bases B and B' when T maps P3 to P4?

    Let T: P3 ----> P4 Im attempting to find the matrix for T relative to the bases B and B' T maps P3 to P4 \begin{array}{l} T(ax^3 + bx^2 + cx + d) = (3x + 2)(ax^3 + bx^2 + cx + d) \\ B = \{ x^3 ,x^2 ,x,1\} \\ B^' = \{ x^4 ,x^3 ,x^2 ,x,1\} \\ \end{array}...
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