Algebra Definition and 999 Threads

I really need help. f(x) is a fourth degree polynomial function f(x) has zeros of plus or minus 2 and plus or minus 3i f(0)=-108 Find an equation for f(x) in general form

I am researching ways linear algebra is integrated into aerospace engineering (I know its alot). I am looking for specific ways. Any help would be appreciated.

1. prove that: X'Y'Z + X'YZ' + XY'Z' + XYZ = (X⊕Y)⊕Z Homework Equations Use postulates and theorems. The Attempt at a Solution X'Y'Z + X'YZ' + XY'Z' + XYZ (original expression) X'Y'Z + X'YZ' + X(Y'Z' + YZ) (distributive) X'Y'Z + X'YZ' + X.1 (complement) X'Y'Z + X'YZ' + X (identity)[/B]...

Homework Statement Homework EquationsThe Attempt at a Solution This whole thing about angular momentum has me totally confused and stumped, but I am trying this problem given in a youtube video lecture I watched. I know of this equation ##L^{2} = L_{\pm}L_{\mp} + L_{z}^{2} \mp \hbar L_{z}##...

Homework Statement Given two arbitrary vectors |\phi_{1}\rangle and |\phi_{2}\rangle belonging to the inner product space \mathcal{H}, the Cauchy-Schwartz inequality states that: |\langle\phi_{1}|\phi_{2}\rangle|^{2} \leq \langle\phi_{1}|\phi_{1}\rangle \langle\phi_{2}|\phi_{2}\rangle...

In math, we normally proceed by learning elementary arithmetic and then elementary algebra. For me algebra is all about assigning a symbol to an unknown value and manipulating it to find its value. Now I don't understand how concepts like groups, fields, rings etc. fall into the algebra...

Hey PF, as my thread a week or two ago said I am currently planning on taking a college Calc and Analytic Geometry class with formal education only up to Geometry. I am very proficient in Geometry, good in algebra 1, have some experience in Trig and a little in Algebra 2. For this reason I was...

In peskin p. 160 forth paragraph they say to verefy Ward identity in equation 5.74. I don't succeed, they say some algebra is needed. I conjecture that this some algebra is what i miss. Any help will be appreciated - thanks a lot.

Apologies if this should be in homework section but I thought it best suited here. Been revising past papers but with no solutions. the following questions all require just a true or false answer. Any help or confirmation of my answers would be appreciated. 1 - every N x N matrix has N...

I know De-Morgan's law that $$ -(p∧q) = -p∨-q $$ Also $$ -(p∨q) = -p∧-q $$ But for material implication and bi conditional operations there are also some transformation. What is the law or proof for it? Like $$ p⇒q = -p∨q $$ $$ p ↔q = (p∧q) ∨ (-p∧-q) $$ There may be other properties also that I...

Homework Statement ##J=r^{2}\dot{\phi}## [1] ##\dot{r^{2}}=E^{2}-1-\frac{J^{2}}{r^{2}}+\frac{2MJ^{2}}{r^{3}}+\frac{2M}{r}##. [2] (the context is geodesic equation GR, but I'm pretty sure this is irrelevant). where ##u=r^{-1}## Question: From these two equations to derive...

Homework Statement [/B] Matrix A = 1 1 0 1 Matrix B = a b c d Find coordinates on a, b, c, d such that AB = BA. Homework EquationsThe Attempt at a Solution I calculated AB and BA with simple matrix multiplication, but am not sure where to go from here. AB = a + c a + b...

Hello everybody, in Schwartz' QFT book it says (p. 483 - 484) In Problem 25.3 this is repeated asking the reader for a proof. I wonder though if this is really true. I know this can be proven for Lie algebras of compact Lie groups (or to be precise, every representation is equivalent to a...

I found out I can pick up a second major in math should I elect to take a two semester sequence in abstract algebra. My first major is in chemical engineering. Right now, I plan on taking a two semester sequence in either: 1) probability with measure theory, 2) abstract algebra (Dummit and...

Let $P$ be a function defined on $[0, 1]$ such that $P(0)=P(1)=1$ and $|P(a)-P(b)|<|a-b|$, for all $a\ne b$ in the interval $[0, 1]$. Prove that $|P(a)-P(b)|<\dfrac{1}{2}$.

Given series:1,2,5,12,25... How did they get :##T_n=a(n-1)(n-2)(n-3)+b(n-1)(n-2)+c(n-1)+d## And for series like 3,7,13,21,... they have given ##T_n=an^2+bn+c## How do you get these equations?

So I have the metric as ##ds^{2}=-(1-\frac{2m}{r})dt^{2}+(1-\frac{2m}{r})^{-1}dr^{2}+r^{2}d\Omega^{2}##* I have transformed to coordinate system ##u,r,\phi, \theta ##, where ##u=t-r*##(2), where ##r*=r+2m In(\frac{r}{2m}-1)## and to the coordinate system ##v,r,\phi, \theta ##, where...

Homework Statement I have the expression [((1-x)/x) * x^(2/1-x)] / x^(2x/1-x) I want to simplify this expression.Homework Equations None The Attempt at a Solution I am not so good with algebra. But I tried to find a common factor for x^(2/1-x)] / (x^2x)/1-x and then add them. However, it...

https://www.quantamagazine.org/20150312-mathematicians-chase-moonshines-shadow/ Sorry for the long title but ST = string theory. Just thought it was interesting news personally since string theory has been elusively hard to prove or observe(at least the particles it claims to predict, notably...

I would like to know some general properties of the modulo (remainder) function that I can use to rewrite expressions. For example, say we wanted to prove the following by rewriting the right-hand-side: $$ \Big{\lfloor} \frac{n}{d} \Big{\rfloor} = \frac{n - n \pmod d}{d} $$ I have no idea how...

Hi I got stuck at the following circuit problem which involves linear algebra, since I am not a physics major, I don't even have the basics to get started. Please shed some light, really appreciate it! Thanks a lot. 1. Homework Statement Consider a long chain of resistors wired up like this...

Hi It's just that last step I'm not getting, so you have: [1 / Kz] - [1 / (2K)z] = [ (2K)z - Kz ] / [(2K)z * Kz] = [ (2)z - 1 ] / [(2K)z*] Then what? Thanks

Let N be a normal subgroup of a group G and let f:G→H be a homomorphism of groups such that the restriction of f to N is an isomorphism N≅H. Prove that G≅N×K, where K is the kernel of f. I'm having trouble defining a function to prove this. Could anyone give me a start on this?

My book says in the slow motion approx, so ## v << c ##, ##v=\frac{dx^{i}}{dt}=O(\epsilon) ## It then states: i) ##\frac{dx^{i}}{ds}=\frac{dt}{ds}\frac{dx^{i}}{dt}=O(\epsilon) ## ii) ## \frac{dx^{0}}{ds}=\frac{dt}{ds}=1+O(\epsilon) ## The geodesic equation reduces from...

This problem is so simple that I'm not exactly sure what they want you to do: Let A and B be n x n matrices such that AB = BA. Show that (A + B)^2 = A^2 + 2AB + B^2. Conclude that (I + A)^2 = I + 2A + A^2. We don't need to list properties or anything, just manipulate. This all seems...

I am trying to learn the formalism of qm, so i am following the book linear algebra done right but is it worth it to study every proof? I mean what is the attitude to follow with such a proof oriented book to eventually have a solid basis in the libear algebra of qm?

Homework Statement Homework Equations A=LU, U^-1 * L^-1= A^-1 , U^-1 * L^-1 * U^-1 * L^-1 = A^-2, The Attempt at a Solution I used MATLAB and the relations: U^-1 * L^-1= A^-1 , U^-1 * L^-1 * U^-1 * L^-1 = A^-2, to find a solution I found U^-1*L^-1 , let =B...

I decide to self-study linear algebra. I have heard words about some good books on this subject such as Sheldon Axler's. Unfortunately his book is only loanable for 4 days in my university library. There is this book from S. Lang that I can borrow for one month, so what do you think about this...

Homework Statement Show that the members of the Lie algebra of SO(n) are anti-symmetric nxn matrices. To start, assume that the nxn orthogonal matrix R which is an element of SO(n) depends on a single parameter t. Then differentiate the expression: R.RT= I with respect to the parameter t...

Homework Statement Show that the given matrices are row equivalent and find a sequence of elementary row ops that will convert A into B. a = 2 0 -1 1 1 0 -1 1 1 b = 3 1 -1 3 5 1 2 2 0 Homework EquationsThe...

Homework Statement "Let L1 be the line having parametric equations : x = 2 - s, y = -1 + 2s, z = 1+s and L2 be the line: x = 1 +t, y = 2+ t, z =2t . a. Do the lines intersect? If so, find the point of intersection. b. Find the point P on the graph of L1 that is closest to the graph of L2...

The question word for word : "Write the equation satisfied by all of the points P(x, y, z) that are at the same distance from the point F(0, 0, 4) and the plane z = 0." I figured I could maybe start by finding the distance between point F and the plane z = 0 but I can't figure out how to...

Homework Statement How do you know if say [(x_1,y_1),(x_2,y_2)] = x_1x_2 + 7y_1y_2 ? or any other equation? Homework EquationsThe Attempt at a Solution

I was given the following as a proof that the inertial tensor was symmetric. I won't write the tensor itself but I will write the form of it below in the proof. I am confused about the steps taken in the proof. It involves grade projections. A \cdot (x \wedge (x \cdot B)) = \langle Ax(x...

Recently I have known an algebraic theorem on polynomial while learning the method of partial fraction. The theorem is : Any polynomial can be written as the product of linear factors and irreducible quadratic factors. I did not find an intuitive proof of this theorem.I asked a question in this...

Warning: This is going to be a bit long. (Apparently my post was too long so it wouldn't render at all. I've split this into two threads.) I worked out some basic Algebraic properties of a Lie Algebra. This is similar to my previous thread about SU(2) but as I don't know this example I'm...

First, let me say that I am a senior physics undergrad. I have failed Linear Algebra once before. Otherwise I am a straight A student. I'm also taking Ordinary Differential Equations right now, and I breeze through that class without a care in the world. I'm not sure if I've developed some sort...

ab'c + a'b + bc' + abc = ac + a'b + bc' (How to further reduce this?) Kmap gives B + AC

I was taught that when you have a polynomial fraction where the denominator is of a higher degree than the numerator, it can't be reduced any further. This seems wrong to me for a couple of reasons. 1. If the denominator can be factored some of the terms may cancel out 2. Say you have the...

Homework Statement Prove that if A, B, and C are square matrices and ABC = I, then B is invertible and B−1 = CA. Homework EquationsThe Attempt at a Solution I think I have this figured out, just checking it. Heres what I got: ABC=I (ABC)B-1=IB-1 (B*B-1)AC=IB-1 I*AC=IB-1 Cancel I using left...

I'm looking at: http://arxiv.org/pdf/gr-qc/9712019.pdf, deriving the FRW metric, and I don't fully understand how the Ricci Vectors eq 8.5 can be attained from 7.16, by setting ##\partial_{0} \beta ## and ##\alpha=0## I see that any christoffel symbol with a ##0## vanish and so so do any...

Homework Statement (a) Show acceleration is perpendicular to velocity (b)Show the following relations (c) Show the continuity equation (d) Show if P = 0 geodesics obey: Homework EquationsThe Attempt at a SolutionPart (a) U_{\mu}A^{\mu} = U_{\mu}U^v \left[ \partial_v U^{\mu} +...

Homework Statement I am confused a little bit. I have been asked to simplify this function: A/B + /BC + /AB I seriously can't seem to know how to simplify this as for me its already simplified. Homework Equations N/A The Attempt at a Solution The best I could do is : (/A+/B) * (A+B+C) I did...

Homework Statement Two pumps of different sizes can empty an entire fuel tank in 4.8 hours. Used alone, the larger pump would empty the tank 4 hours less than would the smaller pump. If using only the smallest pump How long will it take to empty the tank? Homework Equations X = small pump...

Homework Statement Prove that set of all onto mappings of A->A is closed under composition of mappings: Homework Equations Definition of onto and closure on sets. The Attempt at a Solution Say, ##f## and ##g## are onto mappings from A to A. Now, say I have a set S(A) = {all onto mappings of A...

Homework Statement Prove that if A is an n x n matrix with the property A3=A, then det(A)=-1, det(A)=0, or det(A)=1 Homework EquationsThe Attempt at a Solution At first I started with the property A3=A I then applied the determinant to both sides. From this point I don't really see any...

<< Mentor Note -- OP has been advised to type their questions into the forum next time, instead of inserting images >> 1. Homework Statement Dear Mentors and PF helpers, I have a question from today's lesson. Homework EquationsThe Attempt at a Solution Is 1) and 2) both acceptable? If...

Recommend a self study book for linear algebra with complex numbers

I need some help in understanding the reasoning and analysis in the solution to Exercise 4.5 in Robert C. Wrede and Murray Spiegel's (W&S) book: "Advanced Calculus" (Schaum's Outlines Series). Exercise 4.5 in W&S reads as follows: https://www.physicsforums.com/attachments/3918 The...

Now ℝxℝ≅ℂ, seen by the map that sends (a,b) to a + bi. ℂ is a field, so the product of any two non-zero elements is non-zero. However, this doesn't seem to hold in ℝxℝ, since (1,0) * (0,1) = (0,0) even though (1,0) and (0,1) are non-zero. What am I missing? Also, the zero ideal is maximal in ℂ...