Forms Definition and 448 Threads

A question about how find the canonical forms over R and C. An example, given a quadratic form,q(x,y,z)=x^2 + 2xy + 4yz + z^2 find the canonical forms over R and C. First step,i get the matrix 1 2^0.5 0 2^0.5 0 2...

Homework Statement Suppose that the matrix A has characteristic equation (lambda - 2)^3 * (lambda + 1)^2 (a) Write all 6 of the possible Jordan forms of A. (b) Compute det(A) and tr(A). Homework Equations The Attempt at a Solution To figure out Jordan forms I need to find the...

For an odd prime number p let Fp be the field with p elements, ie. the integers {0...,p-1} with addition and multiplication defined modulo p. How many quadratic forms are there on the vector space Fp^n I don even know how to start this question

Hello, I was tempted to put this in the math section but it is more of a visualization problem though it is most likley due to my lack of understanding the divergence and curl operators fully. I am comfortable with the closed loop integral of E dot dA and can visualize it as a solid closed...

Hi all, I am taking this math methods course in grad school, and in the lectures we stormed through differential geometry. My geometry is already horrible, I find it hard to understand all these forms, fields, tensors, wedge products etc... I would be glad if you could suggest some books...

I understand that the truth table involved, and how it works, but i don't get the timing of the diagrams. I've looked on numerous internet sites and through many books but i still don't understand how when J=K=0 and CLK= up, with Q having no change, that the out put (Q) is up, when the others...

The first brains came about in the precambrian or at the border with the cambrian around 560 million years ago when the first multi-celluar organisms emerged. It has always struck me how/why organisms developed brains. The brain must have emerged together with eyesight, since eyesight would be...

If a salt crystal forms after 3 days of evaporation, and the crystal mass is 30 mg, how many Na+ and Cl- ions was added to the crystal each second (average). How do I solve this?

I wonder if anyone has heard of this new (perhaps decades old?) idea I stumbled on. The matter that falls into an event horizon is quickly absorbed. Everyone knows that. But the key difference is what happens later. Underneath the energy barrier, the matter that is consummed is distributed...

I need to pass variables from one form to another for printing purposes. I'm using the PrintForm component to print the form. I'm familiar with this concept using VBScript and .asp... However, I am at a loss for how to do so using VB 2008.

Homework Statement V is a unitarian space of finite dimensions and T:V->V is a linear transformation. Every eigenvector of T is an eigenvector of T* (where (Tv,u) = (v,T*u) for all u and v in V). Prove that T(T*) = (T*)T.Homework Equations The Attempt at a Solution First of all, since the space...

[FONT="Comic Sans MS"]Ok i am having a hard time with this one. Find the product z1z2 in standard form. Then write z1 and z2 in trig form and find their product again. Finally, convert the answer that is in trig form to standard form to show that the two products are equal. z1= 1+i, z2= 4i

I have a problem with determining eigenvalues. This is what I've got thus far: Homework Statement Identify and sketch the graph of the quadratic equation 4x² + 10xy + 4y² = 9The Attempt at a Solution We put it in the matrix form: \begin{pmatrix} 4 & 5 \\ 5 & 4 \\ \end{pmatrix} Now we find the...

it's a bit simple i know but i just forgot how to do it and i need to know its done for an exam next week...i just want to know how to add these two polar form vectors 8.54<69.44 + 4.123<14.036

I've just begun investigating differential forms. I have no experience in this field and no formal, university level training in mathematics, so please bear with me. I understand that a differential form may be thought of as a family of linear functionals; more precisely, it is a function that...

My differential forms book (Flanders/Dover) defines an inner product on wedge products for vectors that have a defined inner product, and uses that to define the hodge dual. That wedge inner product definition was a determinant of inner products. I don't actually have that book on me right...

I have a quetion about the forms. When we say, "differential forms of degree one (or more)" rather than degree zero, the algebra is now mixed with topological properties. Am I correct? I am simply trying to find my way to understand this.

Suppose you have one limit lim_{x\rightarrow \ 0}(cos(x)/x) = \infty and a second limit lim_{x\rightarrow \ \infty}(x) = \infty What is the first limit subtracted by the second? Is it simply indeterminate because its inf - inf? One...

Would this be the right forum to pose questions on this topic?

[SOLVED] Newton's third law Homework Statement My book gives two forms of Newton's Third Law: Weak Form: The forces exerted by two particles \alpha and \beta on each other are equal in magnitude and opposite in direction Strong Form: The forces exerted by two particles \alpha and \beta on each...

If a good sample of dinosaur DNA were found intact, could we make a clone? I know that the chances of finding intact complete DNA of a dinosaur is slim. A researcher recently claimed to have found likely dinosaur dna, although not complete enough for any hopes of cloning or anything. The...

[SOLVED] A formulation of continuity for bilinear forms Homework Statement My HW assignment read "Let H be a real Hilbert space and a: H x H-->R be a coninuous coersive bilinear form (i.e. (i) a is linear in both arguments (ii) There exists M>0 such that |a(x,y)|<M||x|| ||y|| (iii) there...

Consider int(E.dA)=q/e, guass law relating the electric field to the charge enclosed. One can also derive (using the more mathematical version of guass' law - involving the double integral) this same formuala for a graviational field. Here the permitivitty constant would be replaced by...

How can there be three forms of the double-angle formula for cos 20?

Synthetic DNA on the Brink of Yielding New Life Forms

hi i just wanted a quick explanation of what a symmetric matrix is and what they mean by the quadratic form by the standard basis? (1) for example why is this a symmetric matrix [1 3] [3 2] and what is the quadratic form of the matrix by the standard basis? (2) also how would i go...

I searched Google and could not find a solution for this. I have a form with a text box and I want to make it so that when I resize the form while the application is running the text box would get resized as well and be "relative" to the size of the form. Any help please?

1) Let f: V x V -> F be a symmetric bilinear form on V, where F is a field. Suppose B={v1,...,vn} is an orthogonal basis for V This implies f(vi,vj)=0 for all i not=j =>A=diag{a1,...,an} and we say that f is diagonalized. ============ Now I don't understand the red part, i.e. how does...

[SOLVED] Linear forms and complete metric space Homework Statement Question: Let L be a linear functional/form on a real Banach space X and let {x_k} be a sequence of vectors such that L(x_k) converges. Can I conclude that {x_k} has a limit in X? It would help me greatly in solving a certain...

Q: Suppose q(X)=(X^T)AX where A is symmetric. Prove that if all eigenvalues of A are positive, then q is positive definite (i.e. q(X)>0 for all X not =0). Proof: Since A is symmetric, by principal axis theorem, there exists an orthogonal matrix P such that (P^T)AP=diag{c1,c2,...,cn} is...

Hello everyone, I'm new to this forum. I have a doubt about differential forms, related to the divergence. On a website I read this: "In general, it is true that in R^3 the operation of d on a differential 0-form gives the gradient of that differential 0-form, that on a differential 1-form...

Given the vector space consisting of all bilinear forms of a vector space V (let's call it B) it's very easy to prove that B is the direct sum of two subspaces, the subspace of symmetric and the subspace of skew symmetric bilinear forms. How would one go about determining the dimension of these...

I am having problems with understanding the whole concept/how to compute the row-reduced echelon form. Can someone please help me? Thanks

First off, I'm no geometer. I've jumped from looking into QFT from an operator algebra perspective to one looking at it from a differential geometry perspective. It's been a fairly nice ride...modulo the fact that I know very little differential geometry. Thus I have been going through a bit of...

Here's an interesting question. I'm aware of closed forms of cubic polynomials that go through 1 or 2 specific (x,y) points. Are there closed form versions for 3 or 4 points? 1 pt: y = a(x-x_0)^3 + b(x-x_0)^2 + c(x-x_0) + y_0 2 pt: y = a(x-x_0)^2(x-x_1)\ +\ b(x-x_0)(x-x_1)^2 \ +\...

let f:VxV->R be an antisymmetric billinear form in real vector space V, there exists an operator that satisfies J:V->V J^2=-I. i need to prove that the form q:VxV->R, for every a,b in V q(a,b)=f(a,J(b)) is symmetric and definite positive. i tried to show that it's symmetric with its definition...

Hi, I'm seeing that many authors like Griffiths and Halliday/Resnick (I've not seen Jackson and Landau/Lif****z) are deriving the differential form of Gauss's law from the integral form (which is easily proven) by using the divergence theorem to convert both sides to volume integrals and then...

I must comment on the Coulomb force - vectorial & non-vectorial form: F=k*((Q1*Q2)/r^2 ) F=k*((Q1*Q2)/r^2 )*[r] >>>[r] unit vector I know that , in case of vectorial form, I can use superposition principle, and use this form when the direction is important for me. But what's more?

Hi, Earth follws a straight path in 4-d space time.ok.now the Earth moves over the geodesic formed by the sun's gravity.now we also have other 7 planets.So does it mean that the sun forms different geodesic for differnt planets. if my question does make some logic than please explain me.

Hey folks, I'm reading "Symmetry in Mechanics" by S. Singer and I'm stuck on an exercise. It asks to find an antisymmetric bilinear form on R^4 that cannot be written as a wedge product of two covectors. Here are my thoughts thus far: on R^2 its trivial to show that every antisymmetric...

Hi, I don't know if this is the right place to post, but can someone help me understand what differential forms are intuitively? And the wedge product intuitively? And finally, how can they help see the bigger picture of multiple integrals, curls, divergence, gradient, etc. I don't know that...

Greetings, I was wondering what Freud said about the formation of the ego. Like the time of childhood it develops and causes for its formation, thanks.

I am reading some books about differential forms. I don't quite understand what is the geometrical meaning of star (hodge) operator. Can anyone give me a hand please? Leon

Sorry to keep bothering, but I am preparing an exam based on Spivak's book on forms (chapter 7 of tome 1). I need to prove that if \dim V \le 3, then every \omega \in \Lambda^2(V) is decomposable, where an element \omega \in \Lambda^k(V) is decomposable if \omega...

I am looking for some good websites that have proofs involving parallelograms and rhombus'? preferably in statement and reasons format any help would be appreciated. thank you

Hello, I'm interested in starting differential forms, Is this book any good? What audience is it intended for? What prerequisites (E.G. Linear Algebra, Calculus(At what level), etc.) would one need to fully appreciate the scope and depth of information presented in this book? Thanks for...

hi, my question is from Modern Engineering Mathematics by Glyn James pg 177 # 17a Using the exponential forms of cos(theta) and sin(theta) given in (3.11a, b), prove the following trigonometric identities: a) sin(x + y) = sin(x)cos(y) + cos(x)sin(y) and 3.11a is: cos(x) = 0.5*[ e^(jx)...

The question is: Show that on R^2\{0} (without zero), let w=(xdy-ydx)/(x^2+y^2) and show (a) closed (b) not exact. (a) is straightforward, and for (b), the following is the solution lecturer provided. Firstly convert to polar coordinates letting x=rcos(p) y=rsin(p) where p is supposed...

Could someone explain these two concepts? What I need is the big picture of 'why' we need this, roughly 'what' these equations mean, 'where' its used etc Thanks in advance

ello ello! The directions are the following: Rewrite each of the following statements in the two forms \forall x, if ____ then ___ and \forall _____ x, _____ For some reason the latex keeps putting an x for the 2nd form, but it should be Upside down A ______ x, _______ for the...