Product Definition and 1000 Threads

Is the trace of an outer product of a normalized state eq. (psi) equal to 1? Thanks, Chris Maness

1."In this exercise, you will be finding the resultant torque from the cross product of a lever arm with a force vector. The lever arm vector is A=2.0i+3.0j. The force vector is B=3.0i-4.0j. Find A x B B x A and 2A x 3B 2.My teacher has been sick the past few days so hasnt taught us...

Homework Statement In an equilateral triangle with sides u, v, w, where they are all unit vectors, find u dot w. Homework Equations u dot w = |u||w|cosθ The Attempt at a Solution The answer is ##\frac {-1} {2} ## cos(120) = -1/2 Elsewhere, I read the statement that since these are...

Homework Statement I have been sitting here for the last hour trying to figure it out but I can't seem to be able to find what I'm doing wrong. I need to expand an equation. Homework Equations a2 - a - 3 The Attempt at a Solution a2 - 1a - 3 The product is -3 and the sum -1...

If the discrete summation is symbolized by ##\sum## and the continuous by ##\int##, so, by analogoy, the discrete product is symbolized by ##\prod## and you already thought what is the symbol for the continuous product?

I'm taking "physics for engineers" right now - the condensed 4 hour summer course over 7 weeks. I'm doing fine in the class. I feel confident about the ideas and concepts we've covered so far, sure enough, but I'm having a hard time grasping the concept (geometrically at least) of the...

Hi, i was wondering how the following expression can be decomposed: Let A=B°C, where B, C are rectangular random matrices and (°) denotes Hadamard product sign. Also, let (.) (.)H denote Hermitian transposition. Then, AH *A how can be decomposed in terms of B and C ?? For example, AH...

Hi, I'm reading a book about fluid dynamics and I found some strange product between tensors. It's written like this: v=S:∇I , where S and I are matrices and v is a vector. Symbol : usually denotes Frobenius inner product. In this case we have a product of a matrix with a tensor of rank 3 and...

If a system is made up by two subsystems, for example, the atom and the photon. and let's assume the state of the atoms is described by |\phi\rangle, while the state of the photons can be described by |n\rangle, The Kronecker product of the |\phi\rangle and |n\rangle can be used to describe the...

I know intuitively that the Cross Product of two vectors ##\vec{A}## and ##\vec{B}## represents another vector ##\vec{A \times B}## perpendicular to it. In study of physics we come across this situation a lot. Hence I can visualize some applications of it I know that the dot product of...

suppose you have two random variables X and Y which are independent, we want to form a new random variable Z=XY, if f(x) and f(y) are density functions of X and Y respectively what is the density function of Z? I tried taking logs and applying convolution, but it did not really work

Homework Statement Hi all, I'm having trouble evaluating the product g_{αβ}ϵ^{αβγδ}. Where the first term is the metric tensor and the second is the Levi-Civita pseudotensor. I know that it evaluates to 0, but I'm not sure how to arrive at that. The Attempt at a Solution My first thought...

I have: dVμ = (∂Vμ/∂xη)dxη where Vμ is a contravariant vector field I believe the () term on the RHS is a covariant tensor. Is the dot product of () and dxη a scalar and how do I write this is compact form. I know how this works for scalars but am not clear when tensors are involved.

Hi there! Im new to this forum so pardon me if this is the wrong place to post my question. Basically, I have an idea with regards to doing some modification to phone screens. However, there is no such technology (yet) for this and I have zero knowledge and background pertaining to...

Hello I am trying to learn something and really hope to get some help.. i know the use of envelope detector.. but when to use product detector? i know product detector will be more expensive than envelope detector.. please help

Vectors a and b correspond to the vectors from the origin to the points A with co-ordinates (3,4,0) and B with co-ordinates (α,4, 2) respectively. Find a value of α that makes the scalar product a\cdotb equal to zero, and explain the physical significance. My attempt: The scalar product...

Cross product is used to find the perpendicular vector of two vectors. If there is any two vectors in a plane then there is always a perpendicular vector to both of them. So in circular motion if the motion is horizontal then is there a perpendicular force to the object in circular motion?

Hey guys, just trying to understand how the quotient rule is derived, so I head over to wikipedia and saw this: But I'm having some difficulty understanding what goes on between these two steps: Could someone shed some light on this?

I asked this in the logic&probability subforum, but I thought I'd try my luck here. ... Let (A,\mathcal A), (B,\mathcal B) be measurable spaces. Let p be a probability measure on (A,\mathcal A), and let q:A\to\mathcal P(B,\mathcal B) be a measurable function which takes each a\in A to...

Homework Statement I am trying to calculate the flux for the octant of a sphere, and I am trying to figure out how the mathematics, dot products, and dA works in the integral. I already did the quadrant for \hat{θ} where θ= π/2 (the bottom quadrant) and I did the left quadrant where \hat{n}...

Vectors -- dot product and cross product? Hello may i know when to dot product and cross product?? both look to same to me..

Let (A,\mathcal A), (B,\mathcal B) be measurable spaces. Let p be a probability measure on (A,\mathcal A), and let q:A\to\mathcal P(B,\mathcal B) be a measurable function which takes each a\in A to some probability measure q(\cdot|a) on (B,\mathcal B). Then there is a unique probability...

Let's say A and B are 2 vectors with length in cm and the angle between them is 170°. Obviously, the dot product of A and B will give cm2 as unit but since the value of cos(170) is negative, will the dot product be negative (something)cm2?

I tryied make the convolution product between x² and x³ by ##\int_{- \infty}^{+ \infty} f(u) g(x-u) du## and the result is an indeterminate form, however, by defintion ##\int_{0}^{x} f(u) g(x-u) du##, the result is 1/60 x6. So, \int_{- \infty}^{+ \infty} f(u) g(x-u) du \overset{?}{=}...

A spin 1/2 particle A undergoes decay A→B+C+D Where it is known that B and C are also spin 1/2. The complete set of allowed values of spin of D It was a Multiple Choice Question and options given were 1) 1/2,1,3/2,2,5/2,3,... 2) 0,1 3) 1/2 only 4) 1/2,3/2,5/2,7/2,... I tried the...

Hi all. I'm having trouble understanding the cartesian product of a (possible infinite) family of sets. Lets say \mathcal{F} = \{A_i\}_{i \in I} is a family of sets. According to wikipedia, the cartesian product of this family is the set \prod_{i \in I} A_i = \{ f : I \to \bigcup_{i...

I am trying to understand the difference from a physical phenomena point of view, not just math. Surprisingly I think I got the cross product like in rotational momentum. You have the momentum vector and we have effective distance from the momentum vector R that needs to be perpendicular to the...

Dear All, I am unable to understand a simple mathematics relation. I spent 2-3 hours to Google multi-variable mathematics and have studied some concepts, still i am missing/confusing some basics. The problem I have at hand is following. Vector p can be written as p = (p1, p2, p3) = n(sin θ3...

Find : $$ \sqrt{ \frac{1}{2}}\sqrt{ \frac{1}{2} + \frac{1}{2} \sqrt{\frac{1}{2}}} \sqrt{ \frac{1}{2} + \frac{1}{2} \sqrt{ \frac{1}{2} + \frac{1}{2} \sqrt{\frac{1}{2}}}}\sqrt{ \frac{1}{2} + \frac{1}{2} \sqrt{ \frac{1}{2} + \frac{1}{2} \sqrt{\frac{1}{2} +\frac{1}{2}\sqrt{\frac{1}{2}}}}} \cdots...

What will happen to product detector and envelope detector when modulation depth is increasing?

Hey! :o "Let the polynomials $$f(x)=1+\sum_{k=1}^{8}{(2k)x^{2k}} \text{ and } g(x)=1+ \sum_{k=1}^{8}{(3k)x^{3k}}$$ of $\mathbb{Q}$. Without calculating $f(x)g(x)$, find the coefficient of $x^{21}$ at $f(x)g(x)$." Let's consider $f(x)=\sum_{k=0}^{\infty}{a_kx^k}$ and...

Is there an expression, in general, for the product of two matrix exponentials, for non-commuting matrices? i.e. something of the form, e^Ae^B = e^{( * )} where the ( * ) would, I assume, depend in some way on the commutator [A,B] ? I can only find examples online when [A,B] = 0...

Homework Statement This makes intuitive sense to me, but I am getting stuck when trying to read the Dirac notation proof. Anyway, the author (Shankar) is just demonstrating that the product of two operators is equal to the product of the matrices representing the factors. Homework Equations...

Given two coefficient binomials \binom{a}{b} and \binom{c}{d} is possbile to express the sum and product those coefficient binomials as one other?

Hey everyone, This has been bugging me for a bit. I think I'm probably missing something pretty easy. A dot B= ABcos(θ), where θ is the angle between A and B. There is the little shortcut that says where B is the derivative of A, A dot B= AB. Clearly then cos(θ) = 1, and the angle between a...

suppose we consider the measurement operator A=diag(1,-1). Then the tensor product of A by itself is in components : A\otimes A=a_{ij}a_{kl}=c_{ijkl} giving c_{1111}=c_{2222}=1, c_{1122}=c_{2211}=-1 and all other component 0. to diagonalize a tensor of order 4, we write ...

Hi everyone, :) Xristos Lymperopoulos on Facebook writes (>>link<<);

The interpretation of the vector product is the area of the parallelogram with sides made up of a and b and the scalar triple product is the volume of the parallelpiped with sides a, b, and c, but what is the interpretation of the vector triple product. Is it just simply the area of the...

If u × v = u × w, so v = w ?

y=3x2Inx u=3x2 v=Inx du/dx=6x dv/dx=I/x y=u*v dy/dx=(u)(dv/dx)+(v)(du/dx) dy/dx=(3x2)(I/x)+(Inx)(6x) Can I simplify this further

Homework Statement {a_n} and {b_n} are two sequences given by a_n = (x)^{1/2^n}+(y)^{1/2^n} and b_n = (x)^{1/2^n}-(y)^{1/2^n}. Then find a_1 a_2 a_3 ... a_n in terms of x,y and b_n Homework Equations The Attempt at a Solution I tried substituting n=1,2,3 and so on for a few...

"Projection Using Dot Product" "Finding a Force" (Boat Problem) Homework Statement ------------------------------------------------------------------------------------------- A 600 pound boat sits on a ramp inclined at 30 degrees. What force is required to keep the boat from rolling down...

Given pq where p < q are prime, but either (p \equiv 1 \mod 4 and q \equiv 3 \mod 4) or (p \equiv 3 \mod 4 and q \equiv 1 \mod 4). Is there a ppt algorithm that will distinguish the two possibilities?

So the complex exponential Fourier series form an orthonormal basis for the space of functions. A periodic function can be represented with countably many elements from the basis, and an aperiodic function requires uncountably many elements. Given a signal, we can find the coefficients of the...

Cartesian product of indexed family of sets The definition of a Cartesian product of an indexed family of sets (X_i)_{i\in I} is \Pi_{i\in I}X_i=\left\{f:I \rightarrow \bigcup_{i \in I} \right\} So if I understand correctly, it's a function that maps every index i to an element f(i) such...

Hi all, I'm trying to work out how I can get the set at specific index in a cross product without creating the whole product. For instance: I have array A of length 512 I also have a number that specifies how many times that array needs to be 'cross-producted' against itself. This gives me...

Two days ago, I was absolutely certain to have proved the theorem hereafter. But then, micromass pointed out that another theorem the truth of which I was also certain was in fact false. It seems that in mathematics, never be certain until other mathematicians are. This is the reason why I...

Homework Statement Proof that (A×B) . (B×A) + (A . B)^2= A^2 . B^2 Homework Equations A×(B×C)=(A . C)B - (A . B)C The Attempt at a Solution Assuming K=(A×B) K . (B×A) + (A . B)^2 = A^2 . B^2 B . (A×K) + (A . B)^2 = A^2 . B^2 B . [A×(A×B)] + (A . B)^2 = A^2 . B^2 B . [(A . B)A...

Homework Statement Prove that (A×B) . [(B×C)×(C×A)]=(A,B,C)^2 where A, B, C are vectors in R3. Homework Equations W×(U×V)=(W . V) U - (W × U) V The Attempt at a Solution Assuming K=(A×B), M=(B×C): K . [M×(C×A)] K . [(M . A) C - (M . C) A] [(M . A)(K . C) - (M . C)(K . A)]...

We know that: \frac{d}{dx}(\vec{f} \cdot \vec{g}) = \frac{d\vec{f}}{dx} \cdot \vec{g} + \vec{f} \cdot \frac{d\vec{g}}{dt} and: \frac{d}{dx}(\vec{f} \times \vec{g}) = \frac{d\vec{f}}{dx} \times \vec{g} + \vec{f} \times \frac{d\vec{g}}{dt} But, exist some formula (some expansion) for: \int \vec{f}...