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    Tensor product of vector space problems

    Tensor product of vector space problms Homework Statement I'm currently reading Halmos's book "Finite dimensional vector spaces" and I find it excellent. However, I'm having some problems with his definition of the tensor product of two vector spaces, and I hope you could help me clear it...
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    Tensor product?

    Hello, I'm currently reading Halmos's book "Finite dimensional vector spaces" and I find it excellent. However, I'm having some problems with his definition of the tensor product of two vector spaces, and I hope you could help me clear it out. Here's what he writes: "Definition: The tensor...
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    Dual basis problem. (Linear Algebra)

    Homework Statement Prove that if m < n and if y_1,...,y_m are linear functionals on an n-dimensional vector space V, then there exists a non-zero vector x in V such that [x,y_j] = 0 for j = 1,..., m Homework Equations The Attempt at a Solution My thinking is somehow that we...
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    Triple integrals.

    Homework Statement Integrate \int_D z dxdydz where D is z\geq 0, z^2*\geq 2x^2+3y^2-1, x^2+y^2+z^2 \leq 3 Homework Equations Spherical coordinates? I'm stuck. I have problems finding the boundaries of integration. The Attempt at a Solution None. I'd be most grateful for help...
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    Another linear algebra problem, basis and linear transformations.

    Homework Statement The matrix A =(1,2,3;4 5 6) defines a linear transformation T: R^3-->R^2 . Find the transformation matrix for T with respect to the basis (1,0,1),(0,2,0),(-1,0,1) for R^3 and the basis (0,1),(1,0) for R^2. Homework Equations - The Attempt at a Solution I have no...
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    Matrices and bases

    I'm having some trouble understanding basis and how they relate to transformation matrices. Homework Statement Let e_1,e_2,e_3,e_4 be a basis in a four dimensional vector space V. Suppose that the linear transformation F on V has the matrix representation: [1 0 2 1;-1 2 1 3;1 2 5 5;2 -2 1...
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    Linear transformation given a nullspace and a solution space.

    Homework Statement Find if possible a linear transformation R^4-->R^3 so that the nullspace is [(1,2,3,4),(0,1,2,3)] and the range the solutions to x_1+x_2+x_3=0. Homework Equations - The Attempt at a Solution So I thought I should start with trying to find what kind of matrix we...
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    Definition of a derivative in several variables

    Homework Statement Hello, I'm trying to grasp the definition of a derivative in several variables, that is, to say if it's differentiable at a point. My book tells me that a function of two variables if differntiable if: f(a+h,b+k)-f(a,b) = A_1h+A_2k+\sqrt{h^2+k^2}\rho(h,k) And if \rho goes...
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    Complex analysis - prerequisites?

    Hello, I'm thinking of starting a course in Complex analysis and I'm curious, could one start the course without a deep understanding of analysis of several variables? I know how to do curve integrals and such, partial derivatives, double integrals and all that. What prerequisites are there...
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    Vector geometry, some problems.

    I have two problems I need help with. Homework Statement ABCD is a parallellogram. E is the midpoint on BC. F is on AD so that |DF| = 8|AF|. G is the intersection between AE and BF. a) Express the vector AG as a linear combination of u = AB and v = AD. b) Show that the area of the...
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    Easy problem, but no idea how to solve it?

    Homework Statement A motorbike with the velocity 40km/h is able to stop at a distance, D, when it brakes with maximal deacceleration. At what distance will a car with a velocity of 60 km/h stop? Homework Equations . The Attempt at a Solution I was trying to solve it through regular...
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    Good book on mechanics?

    Hello, I'm wondering if anyone has any tips on a good book on mechanics? I'm not too knowledgable in physics, but I do have a good grounding in calculus and linear algebra. Best regards, Magnus
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    Topology - prerequisites

    Hello, I'm wondering, is it possible to study topology without having taken a course in multivariable calculus? I'm very eager to learn and my college don't offer too many math courses this spring (I'm moving to a bigger next fall though), so I'm thinking if I should take topology. I can...
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    Matrices and parameters

    Homework Statement Decide c, so that A(2)X=b(c) where x=(x,y,z) and b(c)=(1,c,1) A(2) is calculated from the previous problem: "Decide the value on the parameter b so that the following system has solutions (2, 1,-1,b 1, 2, 2, 2b 1,-1,-3, b+1) Homework Equations The...
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    Diagonalize a matrix (help for exam)

    Homework Statement Find a matrix that diagonalizes the following 2x2 matrix: A= (1/2 , sqrt(3)/2 sqrt(3)/2,-1/2) What will the diagonalizing matrix D be? What does D mean geometrically? What does A mean geometrically? Homework Equations - The Attempt at a Solution...
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    Linear transformations

    Homework Statement T: R^2-->R2 first rotates points through -3pi/4 radian clockwise and then reflects points through the horizontal x1-axis. Find the standard matrix of T. Homework Equations - The Attempt at a Solution Vector 1 is: (-1sqrt2 - 1 sqrt2) before the reflection, and...
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    Matrices/linear algebra

    Suppose a, b, c and d are constants such that a is not zero and the system below is consistent for all possible values of f and g. What can you say about the numbers a, b, c and d? Justify your answer. Homework Equations ax1+bx2=f cx1+dx2=g The Attempt at a Solution I've been...
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    Size of a black hole?

    How big must a black hole be to swallow an object of 1,5m x 3,585m x 20 cm and how far away must it be to not swallow you and everything around you? It's for a movie a friend is doing, and I really hope that you could answer the question or otherwise give me the formula and you would make my...
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    Newbie maths

    Hey, I'm not advanced in math at all, I only read and finished basic functions. But now,I´m real interested of learning more math, derivates, integrals and other stuff. How could I learn this and is there any way that I can learn more math? I can't take courses :(
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