Identity Definition and 1000 Threads

I've been asked by my professor to identify a group of singular matrices. At first, I did not think this was possible, since a singular matrix is non-invertible by definition, yet to prove a groups existence, every such singular matrix must have an inverse. It has been brought to my...

Can anyone provide me solution to this identity http://books.google.com/books?id=PJeHprppOLsC&printsec=frontcover&dq=complex+variables&hl=en&ei=rFl7TMj0E4P-8AbNgOGFBw&sa=X&oi=book_result&ct=book-thumbnail&resnum=2&ved=0CDYQ6wEwAQ#v=onepage&q&f=false" page 10 , problem 20

Hello, I was looking at some math problems and one kind caught my attention. The idea was to prove that let's say 3x+2y=5 has infinitely many solutions over the integers. Can someone show me the procedure how a problem like this might be solved?

Harmonic function satisfies Laplace equation and have continuous 1st and 2nd partial derivatives. Laplace equation is \nabla^2 u=0. Using Green's 1st identity: \int_{\Omega} v \nabla^2 u \;+\; \nabla u \;\cdot \; \nabla v \; dx\;dy \;=\; \int_{\Gamma} v\frac{\partial u}{\partial n} \; ds...

Homework Statement Attached question Homework Equations The Attempt at a Solution The second part of question is relatively easy, it is the first part of the question where I need help with(using arg zw = arg z + arg w to show arg z^n = n arg z). Also, is the question asking...

Help! I spent 3 hours attempting this question. Prove the following identity : (tan x + sec x -1) / (tan x - sec x + 1) = tan x + sec x I've simplified Left Hand Side into cos and sine. Which ended up like this (sine x - cos x + 1) / (sine x + cos x -1) Then I'm stuck. Any help is...

what do u think of people who have face identity? are they liar or sick? can u trust them? it happens on net a lot that people introduce themselves somebody else. some of them try to impress others by telling lies but i know of so many people who just tell lies about their names...

Homework Statement So we have an observable K = \begin{bmatrix} 0 & -i \\ -i & 0 \end{bmatrix} and its eigenvectors are v1 = (-i, 1)T and v2 = (i, 1)T corresponding to eigenvalues 1 and -1, respectively. Now if we take the outer products, we get these... |1><1| = (-i, 1)T*(i, 1) =...

Homework Statement sin(4x) = 8cos3(x)sin(x)-4sin(x)cos(x) Homework Equations All trigonometric identities The Attempt at a Solution I can simplify the right side using the double angle identity to: sin(4x) = 4sin(2x)cos2(x)-2sin(2x) However, now I'm not sure what to do. Did...

A lot has been discussed/posted about various models/theories to explain consciousness, the systems of laws, fundamental physics, emergence, upward and downward causality etc. However I think too much of these theories focus on GENERAL universals and ultimately on the mechanisms, but not on...

Just wondering how this is simplified to the third line: If w, z are complex numbers wz = rs( cos\alpha + isin \alpha ) (cos \varphi + isin \varphi) wz = rs(cos\alpha cos \varphi - sin \alphasin\varphi) + i(sin \alphacos\varphi + cos \alpha sin \varphi)) wz = rs(cos (\alpha...

Does anyone know how to prove the following identity: \Sigma_{k=0}^{n}\left(\stackrel{n}{k}\right) H_{k}(x)H_{n-k}(y)=2^{n/2}H_{n}(2^{-1/2}(x+y)) where H_{i}(z)represents the Hermite polynomial?

Hi, I start with arctanh\left(\frac{A}{\sqrt{A^2-1}}\right)=\frac{1}{2}ln\left( \frac{1+\frac{A}{\sqrt{A^2-1}}}{1-\frac{A}{\sqrt{A^2-1}}}\right) The function \frac{A}{\sqrt{A^2-1}} is real, and since A>1, it too is always greater than 1. Is it true that it should really be the modulus...

1. By considering, seperately, each component of the vector A, show that \iint A(u.n) ds = \iiint {(u.\nabla)A + A(\nabla.u)} dV (A,u and n are vectors) Homework Equations 3. Attempt at solution L.H.S. Let A = a\vec{i} + b\vec{j} + c\vec{k} \iint (a\vec{i} +...

1. By considering each component of the vector A show that \iint A(u.n)ds = \iiint{(u.nambla)A+A(nambla.u)}dV (A,u and n are vectors) Homework Equations 3. Let A = ai + bj + ck. L.H.S: \iint ai (u.n)ds + \iint bj (u.n)ds +\iint ck (u.n)ds R.H.S. = \iiint(u.nambla)ai dV+...

Is there a shorter way to verify this identity, as you can see I haven't even finished it. I know you can use Ven diagrams and truth tables but I wanted to avoid them inorder to use a more general formal approach. picture is attached

Hello everyone, I would like to ask what's the purpose of identity map? Recently I came across something that apparently use this to find the inverse image of a function F(x) in the form of F(x) = ( f(x) , x ) . Thanks. Wayne

Homework Statement Show using Stoke's Theorem that S is an open surface with boundary C (a space curve). f(\vec r) is a scalar field. Homework Equations Stoke's theorem \iint_S (\nabla\times \vec F) \cdot d\vec S = \int_C F \cdot d\vec r The Attempt at a Solution Thus far...

Homework Statement I did the question with help, but did not understand why did we multiply e^-i(x/2) How do I know what to multiply for getting the real part of a complex number in exponential form? Homework Equations The Attempt at a Solution

Hello, Could you please clarify if this is correct: If tan^(-1)(x) = Pi/2 - tan^(-1)(1/x) Then if we have (ax) as the angle where a is a constant, do we get: tan^(-1)(ax) = Pi/2 - tan^(-1)(a/x) or does the constant go on the bottom with the x? i.e. or: tan^(-1)(ax) = Pi/2 -...

Hi. I'm having trouble trying to understand the relationship between inverse trig functions, especially arcsin x, and pythagorean identity. I know that because cosx=sqrt(1-(sinx)^2), derivative of arcsin x is 1/(cos(arcsin x)) = 1/(sqrt(1-(sinx)^2)arcsinx)) = 1/(sqrt(1-x^2). But how does...

http://www.identitytheft.com/article/are_photocopiers_a_risk

Homework Statement map the function \begin{equation}w = \Big(\frac{z-1}{z+1}\Big)^{2} \end{equation} on some domain which contains z=e^{i\theta}. \theta between 0 and \pi Hint: Map the semicircular arc bounding the top of the disc by putting $z=e^{i\theta}$ in the above formula. The...

Homework Statement Let \mathbf{G}(x,y,z) be an irrotational vector field and g(x,y,z) a C^1 function. Use vector identities to simplify: \nabla\cdot(g\nabla \times (g\mathbf{G})) Homework Equations The '14 basic vector identities' The Attempt at a Solution I tried using the...

Homework Statement Let F(x,y,z) be an irrotational vector field and f(x,y,z) a C^1 scalar functions. Using the standard identities of vector analysis (provided in section 2 below), simplify (\nabla f \times F) \cdot \nabla f Homework Equations Note: The identities below require...

Homework Statement Let f(x,y,z), g(x,y,z), h(x,y,z) be any C^2 scalar functions. Using the standard identities of vector analysis (provided in section 2 below), prove that \nabla \cdot ( f \nabla g \times \nabla h ) = \nabla f \cdot ( \nabla g \times \nabla h) Homework...

One of the basic vector identities is \nabla \cdot (\nabla f \times \nabla g) = 0 Is this true if f and g are C^{1} ? (Or they must be C^{2} functions? Thanks!

Homework Statement Prove the following when p is a positive integer: b^p - a^p = (b-a)(b^{p-1}+b^{p-2}a+b^{p-3}a^2+...+ba^{p-2}+a^{p-1}) Hint: Use the telescoping property for sums. Homework Equations None The Attempt at a Solution I tried reducing it to, (b-a)\sum_{k=1}^p...

Homework Statement Show the following identity (in the sense of distribution): g(\bold x)\delta (\bold x)=g(\bold 0) \delta (\bold x) for a function g. Homework Equations No idea. The Attempt at a Solution I don't have a concrete idea about what a distribution is (It's an...

4/t [cos(wt/2)-1] = -8/t sin(wt/4) ?

Let R be a ring with multiplicative identity 1R. Suppose that R is finite. The elemets xy1, xy2,...xyn are all different. So x y_i=1R for some i. A lemma that is not proven is given. If xyi=1R & yjx=1R, then yi=yj I need to show that yjx=1R. Right now I haven't got much. I took...

After reading an e-mail about a lawyer's identity being stolen and what he did to fight back I thought it was good enough to pass on. See what you think..

Hi, I would like some help in proving the following identity: \sum_{x=0}^{n}x^3 = 6\binom{n+1}{4} + 6\binom{n+1}{3} + \binom{n+1}{2} I tried doing it by induction but that did not go well (perhaps I missed something). Someone told me to use the fact that \binom{x}{0}...

Homework Statement Hi. I need to prove that [b x c, c x a, a x b] = [a, b, c]2 for any three vectors a, b and c. Note that [a, b, c] = a(b x c)Homework Equations I tried using the identify (a x b) x c = (a.c)b - (a.b)c The Attempt at a Solution Using the above identity I got [b x c, c x a...

Hello all, I'm doing a question for the maths module in my physics degree (I'm a second year undergrad) and there's a question I'm doing on basis functions. Homework Statement Verify that functions of the type f_{n}(x) = A cos \frac{2\pi n x}{L} where n = 0,1,2... can be used as a basis...

Say i have a matrix , \begin{bmatrix}{4}&{3}\\{-1}&{7}\end{bmatrix}+5 is it correct if i do it this way , \begin{bmatrix}{4}&{3}\\{-1}&{7}\end{bmatrix}+5\begin{bmatrix}{1}&{0}\\{0}&{1}\end{bmatrix} =\begin{bmatrix}{9}&{3}\\{-1}&{12}\end{bmatrix} is 5 a scalar = 5I where I is an...

Homework Statement prove that: tan(1+cos(x))^2 = 1-cos(x) Homework Equations trig identities, like the pythagorean, sum/difference, double/half angle identities, power reducing identities, etc... The Attempt at a Solution i'm not sure where to start; i tried using the pythagorean...

So I'm given a problem in which I have to prove an identity. It goes: 2csc2x=csc^2xtanx I did the problem myself and could only get to 2csc2x=2\(sin2x)= 2\(2sinxcosx). I had no idea how to get further with the problem so I looked at the answer in the back of my pre-calculus book. It said...

Homework Statement I'm supposed to derive the following: \left({\bf A} \cdot {\bf \sigma} \right) \left({\bf B }\cdot {\bf \sigma} \right) = {\bf A} \cdot {\bf B} I + i \left( {\bf A } \times {\bf B} \right) \cdot {\bf \sigma} using just the two following facts: Any 2x2 matrix can...

Hi, I was looking at an EM problem today and realized I wasn't sure why (kxH)\dotk = 0 I tried writing it out explicitly and got (w 1,2,3 representing directions) A1(A2*B3-A3*B2) - A2(A1*B3-A3*B1) + A3(A1*B2-A2*B1) and I can't see why this should equal zero. This is troubling...

Hi, I'm reading a book at the moment in which the author states the identity: \frac{1}{x-i\epsilon}=\frac{x}{x^2+\epsilon^2}+\frac{i\epsilon}{x^2+\epsilon^2} Which is fine, but then he goes on to state that this is equal to: P\frac{1}{x}+i\pi\delta(x) Where P is the principal...

Homework Statement Find two functions f, g \in C[0,1] (i.e. continuous functions on [0,1]) which do not satisfy 2 ||f||^2_{sup} + 2 ||g||^2_{sup} = ||f+g||^2_{sup} + ||f-g||^2_{sup} (where || \cdot ||_{sup} is the supremum or infinity norm) Homework Equations Parallelogram identity...

Homework Statement Show that for all integers n,m where 0 ≤ m ≤ n The sum from k=m to n of {(nCk)*(kCm)} = (nCm)*2^(n-m) The Attempt at a Solution So for the proof, I have to use a real example, such as choosing committees, binary sequences, giving fruit to kids, etc. I have been...

Cos^2 (wt+a) = 1+Cos(2wt+2a) ?

Hi I've got this problem which has really been bothering me. How are you supposed to prove that: (Sin[A] Sin[2 A] + Sin[3 A] Sin[6 A])/(Sin[A] Cos[2 A] + Sin[3 A] Cos[6 A]) is identicle to tan[5A]. I am almost sure that I've got to use the factor formulae, but I've had no luck. Maybe...

Homework Statement Verify the Identity: cos(x)-[cos(x)/1-tan(x)] = [(sin(x)cos(x)]/[sin(x)-cos(x)] b]2. Homework Equations [/b] reciprocal Identities, quotient Identities, Pythagorean Identities [b]3. The Attempt at a Solution cos(x)-[cos(x)/1-tan(x)] =...

Homework Statement let I_n be as an identity matrix where a_ij = 1 when i=j I just want to ask that is it true that all identity matrix has an inverse (determinant is not 0) for n>=2? The Attempt at a Solution

Hi all, I'm studying my mathematics lesson, and there is an example I can't understand: Consider the matrix A=(0 In) (-In 0) with In the identity nxn We want to compute detA : We introduce the permutation p=(1 2 ... n n+1 ... 2n)...

When you study physics, you never really delve into the reasons behind some of mathematical identities, i was curious about this one as it occurs in Bloch's Theorem (correct me if I go wrong)...

Homework Statement Show |sin z|^2 = \frac{1}{2}[cosh(2y)-cos(2x)]Homework Equations cosh2y = cosh^2y+sinh^2y cos2x = cos^2x-sin^2xThe Attempt at a Solution Here is what I have so far |sinz|^2=|sin(x+iy)|^2=|sin(x)cosh(y)+icos(x)sinh(y)|^2 =sin^2(x)cosh^2(y)+cos^2(x)sinh^2(y)...