Algebra Definition and 999 Threads

I found this video showing an elementary proof of the FTA.

Can anyone tell me if I'm doing this right so far? My question really is... does this mean that the next step for me is to expand the last statement shown?Asking because that seems like a lot of work.

1) Likely an Einstein summation confusion. Consider Lorentz transformation's defined in the following matter: Please see image [2] below. I aim to consider the product L^0{}_0(\Lambda_1\Lambda_2). Consider the following notation L^\mu{}_\nu(\Lambda_i) = L_i{}^\mu{}_\nu. How then, does...

Hi all, I have a problem working out the algebra of the following expression in Peskin & Schroeder in a smart way to give the result. It is on page 191, regarding the numerator of the vertex correction function. We want to get from the LHS to the RHS of the following expression...

The 100W light bulb (cost 0.60 dollars) is not going to be used anymore and is being replaced with the 20W (cost 3 dollars) low energy light bulb. If electricity is charged at $0.15 per kWh, for how many hours must the low energy bulb be used in order for the lower cost of running it to exactly...

I have a matrix equation (left side) that needs to be formatted into another form (right side). I've simplified the left side as much as I could but can't seem to get it to the match the right side. I am unsure if my matrix algebra skills are lacking or if I somehow messed up the starting...

Let the (multi-vector valued) “inner product” between a j-vector U and a k-vector B be defined as the (k-j) grade part of the geometric product UB, (a.k.a. “left contraction”) that is, $$U\cdot B := <UB>_{k-j}$$ (0 when j > k) as is done in Alan Macdonald’s book “Linear and Geometric Algebra.”...

While deriving continuity equation in Fluid mechanics, our professor switched the order of taking total time derivative and then applying delta operator to the function without stating any condition to do so(Of course I know it is Physics which alows you to do so) . So,I began to think...

Can anyone please help me with this equation 3x =15 My workings ;3x=15 Any help is appreciated, thanks = 5x, as 15 divide by 3x=5x

Has anyone taken these two courses online in a self-paced course for credit? If so, where and how was it in terms of quality? How about price? Opinions/thoughts are much appreciated. I'm working and the closest community college is a commute away, so that's out. I'm finding $1100-3000~ for...

I am struggling on how to approach this problem. Hints would help greatly. This is also from Gelfand's Algebra problem 131

Let's say you were proctoring some test that required proofs of Jordan canonical forms and rational canonical forms. Would you dock points from a lazy student abbreviating the former as "J-canonical forms" and the latter as "##\mathbb{Q}##-canonical forms" in their proofs?

When they give reason for multiplication the negative numbers leading to positive number, they base on distribute law.But why the distribute law in algebra is correct like in arithmetic?(e.g why -5(8-6)=-5.8+-5.-6?).In abstract algebra they use distribute law as axiom.But in elementary algebra...

Hi, Could someone help me with this question: 2x – 1 = 9 – 3x Thank you in advance!

One thing I was thinking about doing was to consider these representations as a basis for the gamma matrices vector space, then try to determine what the change of basis from one to the other would be. However I'm unsure if it's correct to treat the representations as a basis, or whether this is...

I need help to know if I'm on the right track: Prove/Disprove the following: Let u ∈ V . If (u, v) = 0 for every v ∈ V such that v ≠ u, then u = 0. (V is a vector-space) I think I need to disprove by using v = 0, however I'm not sure.

8y-2y=6y 6 y+30 6y/6=30/6 Y=5 Now how can I verify this equation?

3m+m=4m 4m +2k =6mk Is this correct, help please if not correct Thanks

have a Summer Exam , at the begging of next week on all topics that we have done , so I decided to do Algebra , but I forgot have to do it , because it was a while ago, can anyone show me the method again please to memorize. Thanks in advance . Workings : add 4x+5=9 3x+6=9 9/3 =3/3 3x=3

Dear Everyone, What are the strategies from proving a either-or statements? Is there a way for me to write an either-or statement into a standard if-then statements? For example, this exercise is from Dummit and Foote Abstract Algebra 2nd, "Let $x$ be a nilpotent element of the commutative...

Here is the initial matrix M: M = \begin{bmatrix} 3 & 1 & 6 \\ -6 & 0 & -16 \\ 0 & 8 & -17 \end{bmatrix} I have used the shortcut method outlined in this youtube video: LU Decomposition Shortcut Method. Here are the row reductions that I went through in order to get my U matrix: 1. R_3 -...

This is the form of the function above: I started by equating (1) to 1/2: $$T(\varphi)=\frac{r^{2}+\tau^{2}-2\tau\cos\varphi}{1+\tau^{2}r^{2}-2\tau r\cos\varphi} = \frac{1}{2},$$ which can be rearranged to: $$2r^{2}+2\tau^{2}-1-\tau^{2}r^{2}=2\tau\left[2-r\right]\cos\varphi$$ using...

My university offers two different two-semester sequences for learning abstract algebra, and I can't decide which one would be better for me, a physics major. Here are the two sequences and their course descriptions, copied and pasted from the university website: Algebra 1: Theory of groups...

I am stuying physics by myself and I would like to get a Computer Algebra System. Does anybody has any suggestions?

March bill was \$400.00 for 25% to be paid of that. There is a recurring overpayment amount of \$85.00 so \$85.00 was to be withdrawn from the 25% of \$400.00 for a total of \$15.00. \$400.00 x .25 = \$100.00 \$100.00 - \$85.00 = \$15.00 However, rather than doing that; the following was...

Hey! :o We have the following equalities: \begin{align*}\left (\overline{y}\land z\lor x\land \left (\overline{z}\lor y\right )\right )\land \left (\overline{x}\lor \overline{y}\right )& \overset{(1)}{=}\left (\overline{y}\land z\lor x\land \overline{z}\lor x\land y\right )\land \left...

Can you help me with this question. 3x=15 Do you have to divide both sides by 3 which, is x=5 Am I right. If not explain please, Thank-you

Is it correct saying that the Exponential limit is an exact solution for passing from a Lie Algebra to a Lie group because a differential manifold with Lie group structure is such that for any point of the transformation the tangent space is by definition the Lie algebra: is that the underlying...

I am currently a community college student majoring in Computer Science, and I was placed into Calculus 1. I had to withdraw from this course for two semesters now. My professor advised me that I have "Algebra Issues". With my weaker foundation of Algebra, I plan to take the College Algebra...

I don't understand this. a is not suppose to be -1; this is the only rule in the equation The answer is the second picture, I just don't know the steps that lead to that answer.

attempt 1. 6 /2×3 = 3×3=3×3=9 attempt 2 6/2(3)= 6 divide 6 = 1. sorry i cannot see the divide symbol.

Monthly Cycle numbers Here is the cycle ratio: $$2_{early}:2_{fertile}:1_{late}$$ And the numbers: $$20,000_{early}:20,000_{fertile}:10,000_{late}$$ Now, let's divide the early into 2 groups, pre-fertile, and safe and assume there is a 50/50 split between those 2 groups. Let's also assume...

My book states the following : ##{\frac{(y_1)-(y_2)}{(x_1)-(x_2)}}*\frac{(3+1)}{(0-0)} = -1## ...(1) ##\implies y_1 - y_2 = 0## (A) Is this a valid deduction? Context : The Problem :If ##A(0,-1)## and ##B(0,3)## are two opposite vertices of a square, then find the other two vertices...

Homework Statement Show that for $$W^\mu = -\frac{1}{2}\varepsilon_{\mu\nu\rho\sigma}M^{\nu\rho}P^{\sigma},$$ where ##M^{\mu\nu}## satisfies the commutation relations of the Lorentz group and ##\Psi## is a bispinor that transforms according to the ##(\frac{1}{2},0)\oplus(0,\frac{1}{2})##...

A monic polynomial of degree N has N number of coefficients. The product of N number of linear factors has N number of free terms. A complex number has 2 DOF. Therefore, both a monic polynomial and the product of free terms have 2N number of DOF of real values. Thus, it must be possible to...

Sorry for the misspelling, but this forum doesn't allow enough characters for the title. The title should be: For the topological proof of the Fundamental Theorem of Algebra, what is the deal when the roots are at the same magnitude, either at different complex angles, or repeated roots? I...

Let a,b,c and n are real numbers.a-b = C I want to get rid of a,b and find the following expression in terms of C and n. How can I do that? (an-bn)= ? (in terms of C and n) Thank you.

why x2 . y2 = (x-y) (x+y) and xy . y2 cannot be (x-y) (y+y)

Let A be a n x n matrix with complex elements. Prove that the a(k) array, with k ∈ ℕ, where a(k) = rank(A^(k + 1)) - rank(A^k), is monotonically increasing. Thank you! :)

I have already taken two elementary linear algebra courses, and have taken the upper-division linear algebra course offered at my school. However, I feel that I did not learn as much from the latter as I should have. I can owe this to not applying myself as much as I should have, due to other...

Are the concepts of the rules of Algebra, Geometry and Probability things that all humans have some instinctive grasp at some level, or things that we basically learn from others, therefore cultural? Let me explain. I once saw an experiment with a mommy rat. She had 4 puppies, and someone put a...

Hi everybody. I am looking for some math books (Algebra Form and Function...Trigonometry...) I found a lot but i don't know how to download it :cry:

I just read through a paper on a \mathbb{Z} _ 3 graded Algebra. In this instance we are talking about color Dirac spinors in space-time. It looks like the author is talking about \left ( SU(3) \otimes L^4 \otimes \mathbb{Z}_2 \otimes \mathbb{Z} _2 \right ) \otimes \mathbb{Z} _3. ( SU(3) is...

Homework Statement Consider the below vector x, which you can copy and paste directly into Matlab. The vector contains the final grades for each student in a large linear algebra course. x = [59 70 83 89 72 70 54 55 68 61 61 58 75 54 65 55 62 39 43 53 67 100 60 100 61 100 77 60 69 91 82 71 72...

Maxwell's equations in differential form notation appeared as a motivating example in a mathematical physics book I'm reading. However, being a mathematical physics book it doesn't delve much into the physical aspects of the problem. It deduces the equations by setting dF equal to zero and d(*F)...

Homework Statement Find the eigenvalues and eigenvectors of the following matrix: $$ A = \begin{bmatrix} 3 & 0 & 0 \\ 0 & 3 & 2 \\ 0 & -1 & 0 \end{bmatrix} $$ Homework Equations Characteristic polynomial: $$ \Delta (t) = t^3 - Tr(A) t^2 + (A_{11}+A_{22} +A_{33})t - det(A) .$$ The Attempt at...

Homework Statement Find the eigenvalues and eigenvectors fro the matrix: $$ A=\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} $$. Homework Equations Characteristic polynomial: ## \nabla \left( t \right) = t^2 - tr\left( A \right)t + \left| A \right|## . The Attempt at a Solution I've found...

Homework Statement This was a coding challenge, and I've already completed it. But I feel there must be a better solution to my approach at the moment. Especially maybe there's a mathematical approach. You have 3 sizes of boxes, small, medium, large: small: holds 3 items medium: holds 5 items...

Hi all, I have stumbled upon Artin's book "Algebra" and was wondering if I could use it to do some self-study on Group Theory. Some background: I am a physics undergraduate who has some competence in elementary logic, proofs and linear algebra. It seemed to me that ideas related to Group...