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...
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...
Homework Statement
Prove that if m < n and if y_1,...,y_m are linear functionals on an ndimensional vector space V, then there exists a nonzero 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...
Homework Statement
Integrate
\int_D z dxdydz where D is z\geq 0, z^2*\geq 2x^2+3y^21, 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...
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...
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...
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...
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...
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...
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 = 8AF. 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...
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...
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
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...
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...
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...
Homework Statement
T: R^2>R2 first rotates points through 3pi/4 radian clockwise and then reflects points through the horizontal x1axis. Find the standard matrix of T.
Homework Equations

The Attempt at a Solution
Vector 1 is:
(1sqrt2
 1 sqrt2)
before the reflection, and...
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...
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...
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 :(