Product Definition and 1000 Threads

Some background: I am self studying dynamics and I have encountered a fundamental problem with either my understanding of linear algebra, or I am just plain dumb. So, I print screened the page of the book we're on. Now let me try to reduce some ambiguity in my question, I have a general...

Homework Statement Let ξm and ηn be vector bundles over a paracompact base space. Show that the stifle-Whitney classes of the tensor product ξm ⊗ ηn (or of the isomorphic bundle Hom (ξm, ηn) can be computed as follows. If the fiber dimensions m and n are both 1 then: w1 (ξ1 ⊗ η1) = w1(ξ1) +...

Here is the question: I have posted a link there to this thread so the OP can view my work.

I have a nice table that shows the dot product between unit vectos (see annex). I'd like know how is the cross product between unit vectos of all basis. Do you have a table with such information?

Prove that $\large 3^{4^5}+4^{5^6}$ is the product of two integers, each at least $\large 10^{2009}$.

Dear all, I've encountered some problems while looking through the book called "Operator Algebras" by Bruce Blackadar. At the very beginning there is a definition of pre-inner product on the complex vector space: briefly, it's the same as the inner product, but the necessity of x=0 when [x,x]=0...

Homework Statement Find the inner product of f(x) = σ(x-x0) and g(x) = cos(x) Homework Equations ∫f(x)*g(x)dx Limits of integration are -∞ to ∞ The Attempt at a Solution First of all, what is the complex conjugate of σ(x-x0)? Is it just σ(x-x0)? And I'm not sure how to...

i realize this is a linear algebra question, but the bra-ket notation is still a little confusing to me so i posted it in this section. |e>=(1+i,1,i) (n-tuple representation, where i's are the imaginaries) so the norm of this would then be the following...

What is the last three digits of the product of the positive roots of $\large\sqrt{1995}x^{\log_{1995} x}=x^2$.

Homework Statement If the 2.0 x 10-5 mol of Cu(IO3)2 can dissolve in 2 L of NaIO3, find the molar concentration of the NaIO3 solution. Ksp = 1.4 x 10-7 for Cu(IO3)2.Homework Equations The Attempt at a Solution Let y = [IO3-(aq)] present in the solution from NaIO3 Cu(IO3)2(s) ↔ Cu2+(aq) +...

Show that \[\prod_{k=2}^{\infty} \left(\frac{2k+1}{2k-1}\right)^{k} \left(1-\frac{1}{k^2}\right)^{k^2}=\frac{\sqrt{2}}{6}\pi \] This problem can be solved using only elementary methods. :D

If $a,b,c,d$ are distinct real no. such that $a=\sqrt{4+\sqrt{5+a}}\;,b=\sqrt{4-\sqrt{5+b}}\;,c=\sqrt{4+\sqrt{5-c}}\;,d=\sqrt{4-\sqrt{5-d}}$. Then $abcd=$

Find the product of all real solutions to the equation $\sqrt{2y-81}-\sqrt{1734-20y+4y^2}-\sqrt{81-2y}+\sqrt{4y^2+26y-129}=0$.

Hey MHB, I am back, fully recover from food poisoning and first off, I want to take this opportunity to wish everyone and their family a very happy and Merry Christmas, much luck, good health and all good things of life. I hope you guys are able to spend it with loved ones!(Inlove) I want to...

Hi All, Have the following given and would like some help with the 3 questions below. Any help will be greatly appreciated :) City 1 TOTAL POPULATION CITY 1 100,000 Avg Age of Population 27.8 Median Age (Male) 20.5 Median Age (Female) 27.8 % Male Population 46.43% % Female Population 53.57%...

I'm so confused about finding an angle, theta in this illustration. With having three coordinate information, how can I calculate the theta using dot product? I would easily find the angle by using trigonometric formula if I ignore the z-axis. But I want to solve this problem with...

I was thinking, if exist a product (cross) between vectors defined as: \vec{a}\times\vec{b}=a\;b\;sin(\theta)\;\hat{c} and a product (dot) such that: \vec{a}\cdot\vec{b}=a\;b\;cos(\theta) Why not define more 2 products that result: \\a\;b\;sin(\theta) \\a\;b\;cos(\theta)\;\hat{d} So, for...

True or False, if AxB = AxC then either A=0 or B=C. A, B, and C are vectors and I thought this statement would be true. However the answer key says it is not. Why?

Hi, Short question: If you take the inner product of two arbitrary wave functions, and then the gradient of that, the result should be zero, right? (Since the product is just a complex number.) Am I missing something? ∇∫dΩψ_{1}*ψ_{2} = 0

I am studying relativity by myself. There is one problem in the book which says that the 4-dot product of the Minkowski force and proper velocity is zero. But again it say that qE.u = change in energy over time. Is there a contradiction? If not, Am I missing something important. here q is...

Homework Statement Given ##S = \{1, x, x^2\}##, find the coordinates of ##x^2 + x + 1## with respect to the orthogonal set of S.Homework Equations Inner product on polynomial space: ##<f,g> = \int_{0}^{1} fg \textrm{ } dx## The Attempt at a Solution I used Gram-Schmidt to make ##S## orthogonal...

Hi, I know these questions must sound ridiculous and I apologize, I'm a newbie. My textbook says that the inner product of the momentum four-vector is P\bulletP=P\bulletP - E^{2}/c^{2}=-m^{2}*c^{2} So my silly questions are: 1) where did the - E^{2}/c^{2} term come from? 2) I know I'm being...

Homework Statement a_n is a sequence of positive numbers. Prove that \prod_{n=1}^{\infty} (1+a_n) converges if and only if \sum_{n=1}^{\infty} a_n converges. Homework Equations The Attempt at a Solution I first tried writing out a partial product: \prod_{n=1}^{N} (1+a_n) =...

Can I say that \eta^{ij}\eta_{km}=\delta^{i}_{k}\delta^{j}_{m}? Kind of in the same way that they yield one delta in the case where one of their indices is summed over? Thanks

Hello I have a set of sets of real numbers greater than 1. Each set can have a different quantity of numbers. Set A1 {a11, a12,...a1m1} Set A2 {a21, a22, ..., a2m2} ... Set AN {aN1, aN2, ..., aNmN} If I want the sum of all possible products that have one element from each set, that's...

The Vector A points 17° counterclockwise from the positive x axis. Vector B lues in the first cuadrant of the xy plane. The magnitudes of the cross product and the dot product are the same: i.e, |AXB|= |A(times)B| What Angle does B make with the positive x axis? 2. Is ti a scalar...

Consider the function APL=\frac{\sqrt[4]{L}}{L}, where L is the number of workers. The company has just hired 8 workers. What is the marginal product of the labor?I know that if I had the total product I could differentiate it and get the marginal product, but it's the average product that is...

Dear Forum : I hung up with a integration http://ppt.cc/mIpV Can it be deduced to a simpler form? The distribution of σ(E) is http://ppt.cc/-5Z5 The estimation width of x is 10MeV , height is 200mb. The distribution of dE/dx is http://ppt.cc/vcVU Is there a way to do some simple...

Homework Statement Assume A and B are normal linear operators [A,A^{t}]=0 (where A^t is the adjoint) show that det AB = detAdetB Homework Equations The Attempt at a Solution Well I know that since the operators commute with their adjoint the eigenbases form orthonormal sets...

I was working on a pde, and I needed to compute a Jacobian for it. Suppose we have a function consisting of a series of matrices multiplied by a vector: f(X) = A * B * b --where X is a vector containing elements that are contained within A, b, and/or b, --A is a matrix, B is a matrix, and b is...

I was working on PDE for a project and needed to compute a Jacobian for it. Suppose we have a function consisting of a series of matrices multiplied by a vector: f(X) = A * B * b --where X is a vector containing elements that are contained within A, b, and/or b, --A is a matrix, B is a...

Hi, So I still not sure how to apply like rhr rule in this setup in problem like the one in the following so I tried to do rhr in order to get the direction but it didn't work out. this is an example from halliday and resnick book. Figure 32-24 shows a wire segment,placed in a uniform...

Just for fun, eh...? (Heidy)For z \in \mathbb{R}, and m \in 2\mathbb{N}+1, show that:\frac{\tan mz}{\tan z}=\prod_{j=1}^{ \lfloor m/2 \rfloor } \tan\left(\frac{j\pi}{m}+z\right) \tan\left(\frac{j\pi}{m}-z\right)

Homework Statement Given 3 measure spaces (X,A,\mu), (Y,B,\zeta), (Z,C,\gamma), show that the product of the three sigma algebras A, B, and C is associative, meaning that: AxBxC=(AxB)xC=Ax(BxC) Homework Equations We can make use of the fact that XxYxZ=(XxY)xZ=Xx(YxZ) The Attempt at a...

I was wondering about the proper way to say, \langleA|B\rangle . I have recently heard, "The inner product of A with B." But I'm not sure if this is correct. Does anyone know the proper order in which to place A and B in the sentence? As a simple example: Suppose you're speaking with...

A simple question: what is the difference between inner product and dot product?

Suppose I was asked if G \cong H \times G/H . At first I considered a familiar group, G = S_3 with its subgroup H = A_3 . I know that the quotient group is the cosets of H, but then I realized that I have no idea how to interpret a Cartesian product of any type of set with elements that aren't...

Let f:\mathbb{R} \to \mathbb{R} and g:\mathbb{R} \to \mathbb{R} be discontinuous at a point c . Give an example of a function h(x)=f(x)g(x) such that h is continuous at c. f(x) = \begin{cases} 0 & \text{if } x \in \mathbb{Q} \\ 1 & \text{if } x \in \mathbb{R}-\mathbb{Q}...

Homework Statement For what values of k is (scalar product of vectors a and b) = a_{1}b_{1}-a_{1}b_{2}-a_{2}b_{1}+ka_{2}b_{2} a valid scalar product? The vectors a and b are defined as: a = a_{1}e_{1} + a_{2}e_{2} b = b_{1}e_{1} + b_{2}e_{2} where e_{1} and e_{2} are unit vectors...

I am currently going through the book Introduction Of Electrodynamics by Griffiths. I have come across vector triple product which is stated as follows in the book: $$\textbf{A} \times (\textbf{B} \times \textbf{C})=\textbf{B}(\textbf{A}\cdot \textbf{C})-\textbf{C}(\textbf{A}\cdot...

Let's say we have operator X that is Hermitian and we have operator P that is Hermitian. Is the following true: [X,P]=ihbar This is the commutator of X and P. This particular result is known as the canonical commutation relation. Expanding: [X,P]=XP-PX=ihbar This result indicates that...

Hi, I was looking for a proof or explanation of this. From Schroeder's Thermal Physics, pg 56, explaining interacting systems in equilibrium. The example in the text is two 3-harmonic oscillators with a total of 6 units of energy. So one macrostate is where each has 3 units of energy. The...

Hello I'm not sure if this belongs in this forum or the homework forum, but I have a quick question about selectivity and yield in reactions where one product is made, and that product returns to one of the reactants to create another separate reaction. for example: C_{6}H_{12} + H_{2}O...

We work on optical simulation where we use not ideal beam expander. Not ideal means that for beam expander designed for single mode (M^2=1), the output beam has M^2 >1 (M^2 = M squared) In our system we want to use beam expander with multimode laser beam. The beam expander is not ideal (for...

Hi, can somebody help me with the problem: Suppose that in a vector space over field of real numbers a positive defined norm is defined for each vector which satisfies the triangle inequality and ||aU||=|a|*||u||. Show that a real valued scalar product can de defined as follows...

Hello, I have a quick question about integrals of dot products. We are learning about magnetic flux as the integral of b dot da. However, what circumstances must be present where we can simplify this integral into (b*a) and ignore the integral?

What is the difference between a dot product and an inner product. The internet says that they are generalizations of each other. What does that even mean? Thanks for any help.

Homework Statement Let \left[a,b\right] be a closed bounded interval, f : [a,b] \rightarrow \textbf{R} be bounded, and let g : [a,b] \rightarrow \textbf{R} be continuous with g\left(a\right)=g\left(b\right)=0. Let f_{n} be a uniformly bounded sequence of functions on \left[a,b\right]. Prove...

How does one change the dot product such that there is no dot product in between, just plain multiplication? For example, in the following: eb.\partialcea=-\Gammaa bc How do I get just an expression for \partialcea?

I would like to know why $M_n$ $\not\cong$ $O_n$ x $T_n$, where $M_n$ is the group of isometries of $\mathbb R^n$, $O_n$ is the group of orthogonal matrices, and $T_n$ is the group of translations in $\mathbb R^n$. **My attempt:** Can I show that one side is abelian, while the other group is...