Algebra Definition and 999 Threads

Homework Statement Let A be an n x n matrix, and let v, w ∈ ℂn. Prove that Av ⋅ w = v ⋅ A†w Homework Equations † = conjugate transpose ⋅ = dot product * = conjugate T = transpose (AB)-1 = B-1A-1 (AB)-1 = BTAT (AB)* = A*B* A† = (AT)* Definitions of Unitary and Hermitian Matrices Complex Mod...

Hi I'm an advanced undergraduate physics student and I'm currently searching books for my career project. The topic I selected is titled: Algebra and geometry in modern physics. So I'm currently looking for books that cover modern aspects of physics in a more mathematical approx. In specific I'm...

This article sounds or reads like the same old problem: http://news.yahoo.com/algebra-unnecessary-stumbling-block-us-schools-170616735.html Why should that be? Students fail algebra 1 either because of lack of effort, lack of motivation, or, if for any student the course is difficult, the...

Hi everyone, I am new here. I know this has been asked before so forgive me, but ima ask again. :) So I'm n pre cal right now and it's going fairly well. I think I'll pass with a B. Next I need to take calculus 1..then later calc 2. So I have 2 options. 1. I can take calculus 1 this summer. I...

Hello Could someone suggest a good book for my son to read to learn algebra? I look in the bookstores and the books titled "Algebra..." all involve equations and unknowns and arithmetic manipulations and train or work problems (2 farmers plow three fields in one day, etc) I am interested in...

Does taking calculus based physics make it fun and more understandable, compared to algebra based physics? It seems like the algebra-based physics you don't go in-depth.

Homework Statement In West Cornwall, I met w women each carrying s sacks, each containing c cats. However, a third of the women then lost half their sacks, and the remaining women lost half their cats from a third of their sacks. How many cats remained, it terms of w, s and c?2. The attempt at...

I'm trying to prove that kinetic energy is not conserved in inelastic collisions using the conservation of momentum. This is the set-up. An object A of momentum ##{m_1}{v_1}## collides inelastically with object B of momentum ##{m_2}{v_2}## using momentum conservation ##P_i = P_f## {m_1}{v_1} +...

Homework Statement In a diagram, P, Q and R lie on a straight line and angle SQR is a right angle. The lengths PS, SR and RP are a, b and c cm respectively and QR is x cm. Use algebra to show that x = (b^2 + c^2 - a^2) / 2c Homework Equations and attempt at a solution[/B] Do I need to use...

Hi, I'm working with series solutions of differential equations and I have come across something that has troubled me other courses as well. given that \begin{equation} \sum_{n=0}^{\infty} c_{n+2}x^n+e^{-x} \sum_{n=0}^{\infty}c_{n}x^n \\ \text{where}\\...

Homework Statement Rocket is accelerating constantly. Let S' be instantaneous rest frame of rocket and S be frame in which rocket is observed moving at velocity v. Homework Equations Given: $$ dv = dv' (1 - v^2) $$ Must prove: $$ \frac{dv}{dt} = \frac{dv'}{dt'} (1 -...

Homework Statement This isn't a homework problem; it's just something I'm working on and I'm a little confused as to how to go about dealing with what I have. I have several traces of Dirac's gamma matrices, and I know that the trace of an odd number of gamma matrices is zero. So my first...

Homework Statement Given an nxn matrix, if a b exists so Ax=b has no solutions, can A be one-to-one? Homework Equations I understand that as a linear transformation, you need things such as (to be one-to-one as a linear trans) 1. n pivots 2. Only the trivial solution exists to Ax=0 Ax=b...

Hey, I need help with part D2. My explanation is not right so I honestly do not know what I am suppose to write. My assignment is attached to this thread.

Homework Statement Suppose X is a set with n elements. Prove that Bij(X) ≅ S_n. Homework Equations S_n = Symmetric set ≅ = isomorphism Definition: Let G and G2 be groups. G and G2 are called Isomorphic if there exists a bijection ϑ:G->G2 such that for all x,y∈G, ϑ(xy) = ϑ(x)ϑ(y) where the...

Hi, I'm looking for a good math book for a 10 year old. He's actually very gifted, as he's able to pick up things like factors and equalities pretty fast. The thing is I'm not a math teacher and I think he needs to go over basic geometry and arithmetic before moving on to algebra, basically...

Homework Statement For the system of springs a) Assemble the stiffness matrix K and the force-displacement relations, K*u = f b) Find the L*D*L^T factorization of K. Use Matlab to solve c) Use the boundary conditions and applied forces to find the displacements Homework EquationsThe Attempt...

Homework Statement I am given the follow graph and asked to find the left null space Homework EquationsThe Attempt at a Solution First I start by transpose A because I know that the left null space is the null space of the incidence matrix transposed. I then reduce it to reduce row echelon...

Homework Statement No official problem, just a study guide fill-in-the-blanks with an extended simplification blank. Basically, no values were given, and it is a standard block on a standard slope with a north-east applied force pushing down on the block (not parallel to horizontal or vertical...

I'm confused about the notation T:R^n \implies R^m specifically about m. From my understanding if n=2 then (x1, x2). Are we transforming n=2 to another value m for example (x1, x2, x3)?

I am trying to build up a kind of mind map of the following: Module (eg. vector space) Ring (eg Field) Linear algebra (concerning vectors and vector spaces, from what I understood) Multilinear Algebra (analogously concerning tensors and multi-linear maps) Linear maps & Multilinear maps The...

C \in \mathbb{R}^{m \times n}, X \in \mathbb{R}^{m \times n}, W \in \mathbb{R}^{m \times k}, H \in \mathbb{R}^{n \times k}, S \in \mathbb{R}^{m \times m}, P \in \mathbb{R}^{n \times n} ##{S}## and ##{P}## are similarity matrices (symmetric). ##\lambda##, ##\alpha## and ##\beta## are...

I'm trying to create a square using algebra tiles. The question is x^2 + 4x + 5. I know how to do it without the algebra tiles but I don't know how to do it with the algebra tiles. Can anyone give me a hand with this?

Homework Statement Hey, I posted another question yesterday, and thanks to the kindness and brilliance of hall of ivy, I was able to solve it. However when I apply the same logic to this new question I cannot seem to get it, can someone explain or show me how to do this question. Consider the...

Homework Statement Consider the linear transformation T from V = P2 to W = P2 given by T(a0 + a1t + a2t2) = (−4a0 + 2a1 + 3a2) + (2a0 + 3a1 + 3a2)t + (−2a0 + 4a1 + 3a2)t^2 Let E = (e1, e2, e3) be the ordered basis in P2 given by e1(t) = 1, e2(t) = t, e3(t) = t^2 Find the coordinate matrix...

Can someone tell me if Axler's texts use proofs? I'm looking for a book that teaches proofs at the high school level. Something other than a geometry text.

Homework Statement Prove that \dim L(\mathbb F)+\dim Ker L=\dim(\mathbb F+Ker L) for every subspace \mathbb{F} and every linear transformation L of a vector space V of a finite dimension. Homework Equations -Fundamental subspaces -Vector spaces The Attempt at a Solution Theorem: [/B]If...

Homework Statement I have these two equations from this paper: https://www.scribd.com/doc/299960566/Spiral Homework Equations What are the vertical bars next to the drawn red starts supposed to indicate in this context? I'm trying to implement these equations into a program but I'm totally...

Homework Statement If gcd(f(x),g(x)) = 1 and m,n ∈ ℕ, show that gcd(f(x)^m, g(x)^n) = 1. Homework EquationsThe Attempt at a Solution So I had previously proved this for non-polynomials: gcd(a,b)=1 then gcd(a^n,b^n)=1 Proof: a = p1*p2*...*pn b = p1*p2*...*pm then a^n = p1^n*p2^n*...*pn^n...

Homework Statement Suppose a field F has n elements and F=(a_1,a_2,...,a_n). Show that the polynomial w(x)=(x-a_1)(x-a_2)...(x-a_n)+1_F has no roots in F, where 1_f denotes the multiplicative identity in F. Homework EquationsThe Attempt at a Solution Strategy: We have this polynomial...

Homework Statement Determine whether the set spans ℜ3. If the set does not span ℜ3 give a geometric description of the subspace it does span. s = {(1, 0, 3), (2, 0, -1), (4, 0, 5), (2, 0, 6)} Homework EquationsThe Attempt at a Solution I am having trouble with the second part of this problem...

Homework Statement 1. Let g(x) = x^4+46. a) Factor g(x) completely in ℚ[x]. b) Factor g(x) completely in ℝ[x]. c) Factor g(x) completely in ℂ[x]. 2. Completely factor the given polynomial in ℤ_5. [4]_5 x^3 + [2]_5 x^2 + x + [3]_5 Homework Equations ℚ = {m/n / m and n belong to Z, m is not...

Hi All, When operating on tables T1, T2 and obtaining a table T3, one obtains rows {##r_{3k}##} in T3 that are obtained from rows {## r_{1i}##} and {##r_{2j} ##} by what I call "concatenation" . I wonder if there is a formal name for it. Specifically, say, during an inner join between T1...

I'm looking for an excellent introductory linear algebra textbook for my second year pure mathematics course. My lecturer highly recommended Introduction to Linear Algebra by Marcus and Minc. She said she has searched for it for many years without success, as it is out of print. I love classic...

Hi all! I have an important decision to make for the summer of 2016 and I need some advice from some who have taken these courses. I need one biology lab elective to graduate, but it is a field lab and it runs from from 5/13 - 6/19. Because it is a field lab, I will not be able to take other...

Dear All Am trying to study supersymmetry algebra. We start by constructing the graded poincare algebra by considering the direct sum of the ordinary Poincare algebra L0 with a subspace L1 spanned by the spinor generators Qa where a runs from 1 to 4 ( L1 is not a lie algebra ). So now we have...

Hi PF! I have a twin brother in the military who is trying to take physics with algebra online (for military purposes he is unable to commute to a University). I thought this course would be easy to find since nearly every school offers calculus online. I haven't been able to find any schools...

How would I solve this using the algebra of sets?

Let $a,\,b,\,c$ and $d$ be positive real numbers such that $(a^2+b^2)^3=c^2+d^2$, prove that $\dfrac{a^3}{c}+\dfrac{b^3}{d}\ge 1$.

Homework Statement Show that all square matrix (A whatever) can be written as the sum of a symmetric matrix and a anti symmetric matrix. Homework Equations I think this relation might be relevant : $$ A=\frac{1}{2}*(A+A^{T})+\frac{1}{2}*(A-A^{T}) $$ The Attempt at a Solution I know that we...

Homework Statement Let g(x) ∈ ℤ[x] have degree at least 2, and let p be a prime number such that: (i) the leading coefficient of g(x) is not divisible by p. (ii) every other coefficient of g(x) is divisible by p. (iii) the constant term of g(x) is not divisible by p^2. a) Show that if a ∈ ℤ...

Homework Statement Find all real numbers k such that x^2+kx+k is reducible in ℝ[x]. Homework EquationsThe Attempt at a Solution This seems like it is simple, but it is new to me so I am looking for confirmation. We know we can find the roots of a polynomial with b^2-4ab. We want b^2-4ab to be...

Homework Statement Let T:R-> S be a homomorphism of rings. Show that T(0_r) = 0_s. Homework EquationsThe Attempt at a Solution First off, the terminology used is kinda confusing. I take 0_r to be the zero in R. Is this correct? For some reason I recall my teacher quickly saying that it was...

Homework Statement Check if L(p)(x)=(1+4x)p(x)+(x-x^2)p'(x)-(x^2+x^3)p''(x) is a linear transformation on \mathbb{R_2}[x]. If L(p)(x) is a linear transformation, find it's matrix in standard basis and check if L(p)(x) is invertible. If L(p)(x) is invertible, find the function rule of it's...

I'm learning geometric algebra. There is a very simple statement which I think is wrong. But it must be right, because all the experts say so. Arrg! The only properties used are 1a = a1 = a aa = 1 if b<>a then ab = -baTheir claim is that abcdabcd = -1. Let's see: aa = 1 abab = -abba =...

Homework Statement Let U is the set of all commuting matrices with matrix A= \begin{bmatrix} 2 & 0 & 1 \\ 0 & 1 & 1 \\ 3 & 0 & 4 \\ \end{bmatrix}. Prove that U is the subspace of \mathbb{M_{3\times 3}} (space of matrices 3\times 3). Check if it contains span\{I,A,A^2,...\}. Find the...

Hello, I'm looking for an algebra based physics book with challenging problems. The reasons is because I'm preparing for an exam (in two weeks time) which will have algebra based physics. Here are the topics: 1. Kinematics 2. Dynamics (Newton's laws, Momentum , Work & Energy) 3. Gravitation 4...

Hey everyone, I am currently taking College Physics I which covers basic mechanics, Newtonian physics, and some other various topics. It is algebra based, as I didn't have physics in high school. I was wondering if there are any good YouTube channels that you all find helpful? I normally watch...

Homework Statement Let R be a ring and suppose r ∈R such that r^2 = 0. Show that (1+r) has a multiplicative inverse in R. Homework Equations A multiplicative inverse if (1+r)*x = 1 where x is some element in R. The Attempt at a Solution We know we have to use two facts. 1. Multiplicative...

Homework Statement Suppose R is a commutative ring with only a finite number of elements and no zero divisors. Show that R is a field. Homework Equations Unit is an element in R which has a multiplicative inverse. If s∈R with r*s = 1. A zero divisor is an element r∈R such that there exists...