Algebra Definition and 999 Threads

Homework Statement The vectors that are perpendicular to (1,1,1) and (1,2,3) lie on a ____. Homework Equations The Attempt at a Solution This is really straight forward, but I cannot validate the answer to myself. The textbook says that they should lie on a line, but why is this? Obviously if...

Is it a must to know clifford algebra in order to derive the dirac equation? I recently watch drphysics video on deriving dirac equation and he use two waves moving in opposite directions to derive it, without touching clifford algebra. If this possible, what is the intuition behind it?

<<Mentor note: Please always use descriptive thread titles.>> First of all, the title is such that it attracts most views.You see, in class our professor did some goofing around numbers and variables in the relativistic energy momentum relation: E2=(pc)2+m02c4 Since the energy required to...

1. Are uncountable unions of sigma algebras on a set X still a sigma algebra on X? 2. Are uncountable intersections of sigma algebras on a set X still a sigma algebra on X? (I think this statement is required to show the existence of sigma algebra generated by a set) 3. If 2 is true, can we...

Hello loves, I know there are post very very similar to this, but I just needed some help understanding it. any help is truly appreciated. 1. Homework Statement A model rocket is launched straight upward with an initial speed of 50 m/s. It accelerates with a constant upward acceleration of 30...

HI all, I am working my way slowly through some classical mechanics books, and I don't think I could function without my CAS (most often my trusty HP 50g, sometimes Giac/Xcas). I have never been very good at pages of algebra, often dropping negatives or whatever, bad enough that working...

Entering my third year of my bachelor of science majoring in maths/physics and having some trouble deciding what courses to do this semester. I know for sure I will be taking complex analysis and 3rd year quantum however am having trouble picking between 3 in particular for my final two courses...

Is there anywhere that teaches tensor analysis in both tensor and non tensor notation, because I'm having to pause each time i look at something in tensor notation and phrase it mentally in non tensor notation at which point it becomes staggeringly simpler. Any help apreciated

Hi all, I am taking Quantum Mechanics II this coming spring semester. However, I haven't taken Linear algebra yet but I don't want to take the class just because for some few topics. What linear algebra topics should I learn before the class? Thanks!

Homework Statement A line is perpendicular to the line 2x - 4y + 7 = 0 and that passes through the point P(7,2). Determine the equation of this line in Cartesian form. Homework Equations n/a 3. The Attempt at a Solution Okay, so how I generally believe how to solve these problems may be...

for this question i got up to obtaining [1 0 1 a-c; 0 1 1 c; 0 0 0 b-a+c] matrix im supposed to find a b and c so that the linear system has an infinitely many solutions I just can't work this out!

I am working through linear algebra from MITs MOOC online courses. One of the question refers to the uncertainty principle. It states: AB-BA=I can happen for infinite matrices with A A=A^{ T }\\ and\\ B=-B^{ T }\\ Then\\ x^{ T }x=x^{ T }ABx-x^{ T }BAx\le 2\parallel Ax\parallel \parallel...

Why, when a fraction has repeated linear terms in its denominator e.g. (11x2+14x+5)/[(x+1)2(2x+1)] does it have to be split into three partial fractions, A/(x+1) + B/(x+1)2 + C/(2x+1)? When my first saw this example, my initial reaction was to split it into A/(x+1)2 +B/(2x+1), but after working...

Let $\mathbb F_q$ be a finite field and let $e, k$ be positive integers with $k \leq e < q-1$. Define $T_e$ to be the set $$T_e:=\left\{p(x) \in \mathbb F_q[x] \;|\; \deg p =e \;, lc(p)=1, \; p(x)|x^{q-1}-1 \right\}. $$ I would like to find the value $$ M(e,k,q):=\max\left\{ | W \cap T_e|...

Dear Physics Forum personnel, I am a college sophomore with double majors in mathematics and microbiology. I apologize for this interruption but I wrote this email to seek your advice and recommendation on linear algebra textbook. I will be taking the "theoretical, proof-based" introductory...

Hiya. Im having problems with Questions 2.(c,i),(c,ii) and (c,iii) question on this past exam paper. http://www.nzqa.govt.nz/nqfdocs/ncea-resource/exams/2014/91261-exm-2014.pdfCan someone check my answers and explain the questions where I face planted? Thanks! 2. (c,i). I got h/(rx-t) = x, I...

Dear all, I am trying to understand the fundamental theorem of algebra from the text (Alan F. Beardon, Algebra and Geometry) attached in this post. I have understood till the first two attachments and my question is from the 3rd attachment onwards. I will briefly describe what...

I'm stuck on deriving the follow. Context: FRW Metric, dust dominated universe, use of conservation of energy-momentum tensor. I'll now state all the equations I can see are relevant. (But just in case the source is http://arxiv.org/pdf/gr-qc/9712019.pdf and it's eq 8.43). ## \frac{d}{dt}(\rho...

Homework Statement In Game 6 of a 6-team double-elimination tournament, Team 1, the top-ranked team, faces the loser of a previous game involving Team 2, the second-ranked team, against one of either Team 3, the third-ranked team or Team 6, the sixth-ranked team. This exercise tests the limits...

I am currently studying A level Further Pure Mathematics, and I will be joining university next year. I want to brush up on precalculus (algebra, trigonometry, geometry) and calculus (differential, integral [single variable]), except that this time I need a more rigorous treatment of those...

I am planning my courses for next semester, and I am unsure of which direction to go in with linear algebra. I have already taken the following course: Linear Algebra I Properties and applications of vectors; matrix algebra; solving systems of linear equations; determinants; vector spaces...

Homework Statement Please refer to : http://math.stackexchange.com/questions/1068948/how-to-prove-that-int-0-infty-sinx-arctan-frac1x-mathrm-dx-fra/1069065#1069065 The answer by @venus. What is the procedure in converting that single integral, dividing it into parts, and making it a double...

Homework Statement In the text, the products pq and qp of the permutations (2 3 4) and (1 3 5) were seen to be different. However, both products turned out to be 3-cycles. Is this an accident? Homework Equations p=(3 4 1)(2 5) q=(1 4 5 2) where p and q are permutations The Attempt at a...

How to find ##\sqrt{(a+b) + 2 \sqrt{ab}} = \sqrt{a} + \sqrt{b}## ?

Homework Statement A series of 5 measurements of Y are recorded with increasing X. (i.e. gradient has units Y/X) The error in measurement of Y is ±0.05 The error in measurement of X is ±0.005. How is the error in the gradient calculated? Homework Equations - measurements[/B] Y | X...

Hey there, I'm thinking about if one of the eigenvalues is zero (means determinant is 0. right?) So, is there any possibility to non-zero eigenvalue also exists?

Can someone please explain why the F( X, Y ) is XY' + XY ? IMO , it is X'Y' + X'Y +XY' +XY ... or the author simplified it to become XY' + XY ? how to simplify it?

Homework Statement Let Hom(V,W) be the set of linear transformations from V to W. Define addition on Hom(V,W) by (f + g)(v) = f(v) + g(v) and scalar multiplication by (af)(v) = af(v. If V is a vector space over a field K, define V* = Hom(V,K). This is called the dual space of V. If...

In Srednicki's text on quantum field theory, he has a chapter on quantum Lorentz invariance. He presents the commutation relations between the generators of the Lorentz group (equation 2.16) as follows: $$[M^{\mu\nu},M^{\rho\sigma}] =...

Homework Statement If the coefficient of kinetic friction in the previous problem was actually 0.11 and the slope 30 degrees, to the nearest meter how far up the hill does he go? **the problem prior was: A skier traveling at 31.9 m/s encounters a 12 degree slope. If you could ignore friction...

I was enrolled in College Algebra for this upcoming winter because the hours will overlap with the class that I enrolled for spring. The reason why I want to learn this, is to refresh my Algebra skills, since I forgot most of it (I only remember matrices, radicals and identities). The purpose...

The title may seem a little confusing and possibly stupid :D What I mean is like a plane doesn't go through the origin? Can we describe a basis for this? If so, how?

2m+(50s)(0.5m/s) = 2m + 25m/{s}^{2} = Not possible My teacher keeps saying this is pure piffle and shaking his head. Can someone please explain this to me?

Homework Statement Let V be a finite dimensional vector space over ℂ . Show that any linear transformation T:V→V has at least one eigenvalue λ and an associated eigenvector v. Homework EquationsThe Attempt at a Solution Hey everyone I've been doing sample questions in the build up to an exam...

Homework Statement Let V be a finite-dimensional real vector space with inner product <⋅,⋅> and L: V → R a linear transformation. Show that there exists a unique vector a ∈ V such that L(x) = <a,x>. Homework Equations Hey everyone, so I'm a physics student who had to choose a few electives in...

I'm a second year student at university studying mathematics. I'm having troubles deciding between a few modules and I hope you can help. http://www.ucl.ac.uk/maths/courses/undergraduates is where all the modules are, please take a look at "Honours Year 2" I get to choose four modules, and so...

Not quite sure, could someone kindly explain the concept of the topic to me? Thanks, it really means a lot. :)

I am in Calculus BC in high school right now and I am really enjoying it and have finished all of the material for the year and I have heard different things about what class comes after Calculus BC (I believe BC is equivalent to Calc 1 & 2 in college). I have heard the next class, aka Calc 3...

Hey, I am a freshman in High School and I have a very superior IQ but I am in normal classes. This is due to ADHD and I used to be lazy in school. Anyways, algebra 1 is VERY boring. I want to teach myself geometry, algebra 2, Pre Cal, and Calculus because I love math. Also I feel like it will...

Homework Statement As a string in my program. Homework Equations Solving a system with the forward phase of row echelon reduction and a consecutive back substitution. All done by numpy here. (The book suggested MATLAB, etc). The Attempt at a Solution import numpy """ In a wind tunnel...

1- How can infer from the determinant of the matrix if the latter is real or complex? 2- Can we have tensors in an N-dimensional space with indices bigger than N?

< Mentor Note -- thread moved to HH from the technical math forums > My final assignment in graduate algebra is to write an essay about the relationship among the subjects we have learned so far this semester: (1) Module (2) The Field of Fractions of an Integral Domain (3) Integrality (4)...

Hello, I'm debating between taking either abstract algebra, theory of numbers, or intermediate symbolic logic as a math elective. Does anyone have any idea which would make my life easier?

Homework Statement [/B] A 0.20-kg block and a 0.25-kg block are connected to each other by a string draped over a pulley that is a solid disc of inertia 0.50 kg and radius 0.10 m. When released, the 0.25-kg block is 0.30 m off the ground. What speed does this block have when it hits the ground...

Homework Statement 4*(5^x)-3(0.4^2x)=11 In case it doesn't make sense, in the attempted solution it's written out better Homework EquationsThe Attempt at a Solution http://imgur.com/SnpFQZV Thanks!

Homework Statement Given that the force of gravitation between Planet A (the one in the left side of the drawing), Fa=3000/da2 and the force of gravitation between Planet B and the rocket, Fb= 6000/ db2. Assuming that the three bodies involved is in stationary. What are the distances (ranges)...

https://www.amazon.com/dp/1133949010/?tag=pfamazon01-20 https://www.amazon.com/dp/1285057090/?tag=pfamazon01-20 https://www.amazon.com/dp/1133959741/?tag=pfamazon01-20 So I'm planning on buying the books in the links above (Algebra and trig, precalc and calc by Ron Larson), but as they are...

In the same way one can show that \nabla^{2}\theta=0 has only one smooth solution, namely \theta=0, I would like to show that \gamma^{i}\partial_{i}\epsilon=0 has only one smooth solution, where \gamma^{i} is a Dirac gamma matrix (or an element of the Clifford algebra), and \epsilon is a...

Homework Statement I stated this as a small attached photo, since i still need to learn to write in latex (see photo) Homework Equations How do you transform the first expression into the next expression (on photo)? The Attempt at a Solution [/B]I tried various manipulations with potens...

Homework Statement Hello there everybody! I'm reading a Linear Algebra textbook, specifically on LTV systems solutions. I'm trying to redo this example from the book: Homework Equations But I couldn't understand the passage: The Attempt at a Solution I mean. x1(0) = 1 and x2(0) = 0? I...