Product Definition and 1000 Threads

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

I understand that the cross product, in lay mans terms doesn't exist unless we're in 3 dimensions. When you multiply two matrices together I have been told you get something similar. I hear that this is because a matrix can be treated as a vector. So if we are talking about measurable...

Factor $5^{1985}-1$ into a product of three integers, each of which is greater than $5^{100}$.

It is known that:\mathcal{F}\{f\ast g\}=\mathcal{F}\{f\}\mathcal{F}\{g\}\mathcal{F}\{f g\}=\mathcal{F}\{f\}\mathcal\ast{F}\{g\} But this property is valid for inverse tranform too?\mathcal{F}^{-1}\{F\ast G\}=\mathcal{F}^{-1}\{F\} \mathcal{F}^{-1}\{G\}\mathcal{F}^{-1}\{F...

Evaluate $\left|\dfrac{2017}{2013}\times \dfrac{2009}{2005}\times \cdots \times \dfrac{49}{45}\times \dfrac{41}{37}\times\dfrac{33}{29} \right|$.

Can someone check my working. I don't understand why i am getting different answers? u(x,t)=\frac{{e}^{-\frac{x^2}{4Dt}}}{\sqrt{4Dt}} Differentiate w.r.t 't' by quotient rule: \frac{\partial u}{\partial t}=\left[ \frac{1}{\sqrt{4Dt}}\cdot \frac{x^2}{4Dt^2}\cdot...

First, thanks to both Deveno and ThePerfectHacker for helping me to gain a basic understanding of tensor products of modules. In a chat room discussion ThePerfectHacker suggested I show that $$ {\mathbb{Z}}_a \otimes_\mathbb{Z} {\mathbb{Z}}_b $$ where a and b are relatively prime integers -...

Hello, The product of a 2x5 matrix P and a 5x3 matrix B shall be a 2x3 zero matrix. P and B are all matrices of integers. P = [6 2 -5 -6 1;3 6 1 -6 -5] One possible B is [0 -4 0;3 0 0;-1 -1 3;2 -3 -2;1 1 3] This solution B has a property: det(PPt) = det(BtB) = 7778 The question is: What...

Homework Statement Find an expression equivalent for the derivative of the scalar triple product a(t) . (b(t) x c(t))The Attempt at a Solution Initially I figured since whatever comes out of B X C is being dotted with A, I can use the derivative rules of a dot product: (a(t)' . (b(t) x...

Homework Statement Let A and B be 4-vectors. Show that the dot product of A and B is Lorentz invariant. The Attempt at a Solution Should I be trying to show that A.B=\gamma(A.B)? Thanks

mathematical "connection" in the cartesian product What is the mathematical connection between elements of a cartesian product ##A\times{}B## and the elements of the sets ##A## and ##B##? In other words, what is the difference between the set ##A\times{}B## and just any set ##Z## with...

Homework Statement You are given that with x = (x1,x2), y = (y1,y2), the formula (x,y) = [x1 x2] [2 1;1 2] [y1;y2] (where ; represents a new row). is a inner product for the vectors in R2 Using this inner product, find a unit vector perpendicular to the vector (1,1) Homework Equations The...

Hi everyone, What does \int \vec{f} × \vec{dl} mean? does it mean "The Line Integral of Vector Function on a positive curve L"? And are the following named correctly? \int \vec{f} . dl : Scalar Line Integral of a Vector Function \int udl : Line Integral of a Scalar Function

I'm not sure which section is best to post this question in. I was wondering if the expression (u $ ∇) is the same as (∇ $ u). Here $ represents the dot product (I couldn't find this symbol. ∇=del, the vector differentiation operator and u is the velocity vector or any other vector

Homework Statement The value of 3i(dot)(jxk) Homework Equations The Attempt at a Solution I know the answer is 3, but could someone please explain how to work this problem?

Problem 1: Let S1 be a sphere centered at(0, 1, -3) with radius 1 and let S2 be a sphere centered at (3, 5, -9) with radius 2. Find the distance between the two spheres. problem 2: Given three non-zero vectors v1, v2, v3 we say that they are mutually orthogonal when v1 dot v2= 0, v1 dot v3=0 ...

Homework Statement The dot product of.two vectors is -1which of the following statements is true A. They must be unit vectors pointing in opposite directions. B. They must be unit vectors pointing j. The same direction. C. They must be more than 90( and less than 270 )degrees from each...

I'm trying to solve the product log of (- (3/2) * e ^(3/2) ) as shown in the link below. http://www.wolframalpha.com/input/?i=product+log+of+%28-+%283%2F2%29e^%283%2F2%29%29 This is a complex number of about 1 + 2i. Should I ignore the complex part of the value and is the value (of...

Homework Statement Show that the dot product in two-dimensional space is linear: <u|(|v> + |w>) = <u|v> + <u|w> The Attempt at a Solution I feel like I'm missing some grasp of the concept here ... I would think to just distribute the <u| and be done in that one step, but I'm being...

hey pf! can someone please explain physically what the dyadic product represents: \vec{a} \vec{b} i know its a matrix (tensor), but that's all i know physically. thanks!

Find y' y=(x2+1)7(x9+2)5(x3+1)3(x8+7)3 Is there a shortcut to doing this problem? Or do I have to actually use the product rule more than 3 times?

Homework Statement So I am not sure how to multiply these two (A*R^2) together. Homework Equations A=( x^2 + y^2 + z^2 ) (xe + y e + z e ) Where x represents the three vector compones I also have R^2=x^2+y^2+z^2 The Attempt at a Solution Is the product of A (x^3e + y^3 e + z^3...

Exist an geometric interpretation for the multiplication of 2 angles? Or exist an geometric interpretation for the square/cube of an angle?

I have been asked to solve the equation for x - All letters bar λ are vectors. λx + (a cross x) = b I have worked it down as far as x.(λb + (b cross a)) = |b|^2 by taking the dot product with b of both sides. But is there any way I can now solve this equation for x?

I was developing a pythagorean theorem proof based on the cross product of two vectors..Below is my final solution...My problem is I had to get around using the distance/magnitude formula because that is using the pythagorean theorem to prove the pythagorean theorem. But after searching, it may...

Homework Statement In 1993 the radius of Hurricane Emily was about 350 km. The wind speed near the center ("eye") of the hurricane, whose radius was about 30 km, reached about 200 km/h. As air swirled in from the rim of the hurricane toward the eye, its angular momentum remained roughly...

Hi guys, I'm not sure how to evaluate this inner product at step (3.8) I know that: ##\hat {H} |\phi> = E |\phi>## <E_n|\frac{\hat H}{\hbar \omega} + \frac{1}{2}|E_n> <E_n| \frac{\hat H}{\hbar \omega}|E_n> + <E_n|\frac{1}{2}|E_n> I also know that ##<\psi|\hat Q | \psi>## gives the...

Homework Statement That is prove that |a•c|≤|a||c| for any vector a=<a1,a2,a3> & c=<c1,c2,c3> Homework Equations The Attempt at a Solution I really don't have much of an attempt at the solution. I am not sure where to start. I can kind of justify it in my mind by saying the...

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...

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) =...