Multiplication Definition and 484 Threads

Find the Laurent Series around z=0 for f(z) = \frac{{2{z^2}}}{{2{z^2} - 5z + 2}} + \sin (\frac{3}{{{z^2}}}), so that the series absolutely converges in z = -i The Attempt at a Solution The singularities of f are z = 0, z = 1/2 and z=2. The Laurent series will converge absolutely in z = -i...

Homework Statement Find the expression of the Laurent series for f(z) = \frac{z}{{(2z - 1)(\frac{2}{z} - 1)}} so that \sum\limits_{ - \infty }^\infty {{a_n}} \ converges. The Attempt at a Solution First, I find that z = 1/2 and z = 2 (and infinite) are poles of the function f. Then, I...

hey guys, <n|(a-+a+)^4|n> = 5n2+5n+3 I am wondering if some one can show me why left and right side are equal 　　　　Thanks in advance

Homework Statement Multiply the permutation (246)(12)(47) The Attempt at a Solution This has got to be so easy yet I cannot figure it out on my own. I understand that for (246) it means that 2 \mapsto 4, 4 \mapsto 6, 6 \mapsto 2 . Could anyone lead me on what I should do next with...

Homework Statement If AB = BA and p is a nonnegative integer, show that (AB)^p = (A^p)(B^p) Homework Equations N/A The Attempt at a Solution I would love to attempt a solution, but I don't even know where to begin. I guess my first question is, how can I generalize matrices so...

Can somebody please explain to me when matrices commute? I've read that it's when they are diagonal with the same dimensions (and also scalar multiples?), but I don't understand why this is.

Homework Statement Compute [1 1]^n [ 1] This is what my book has. I am assuming the blank means 0 (please tell me if this is not the case). Homework Equations None really (matrix multiplication) The Attempt at a Solution I did n = 1, 2, 3, 4 and found a patten. It looks...

Homework Statement I am trying to prove an identity and in order to finish the proof i need to show that: for z a p-dimensional vector and A a non-singular square (pXp) matrix - also note that T is transpose - : zTA^(-1)z = zzTA^(-1), where -1 denotes the inverse I have looked...

I can solve: (2x+3y-4z)(2x-3y+4z) = [2x +(3y-4z)] [2x -(3y-4z)] = (2x)^2 -(3y-4z)^2 = (2x)^2 - (9y^2 - 24yz - 16z) = 4x^2 - 9y^2 + 24yz + 16z which is fine, but if I try to solve: (m^2-m-1)(m^2+m-1) = [m^2 -(m+1)][m^2+(m-1) = (m^2)^ 2 - (m-1)^2 = (m^2)^2 - (m^2 -2m +1) = m^4 - m^2 +2m -1...

Are there any tricks other then adding X by Z in the multiplication chart? Like the one for ten. When multiplying a number by ten all you do is add a zero.

In the appendix B of Goldstein's classical mechanics (3rd edition), the authors discussed the dihedral group and said: "Notice how the group elements in class 3 involve only \sigma_1 and \sigma_3. Thus, they are independent of the matrices I and \sigma_2, as is expected from the structure of...

I am trying to compute the following, \prod_{j=0}^{N-1}\left[\hat{I}+\hat{M(j)}\left(\frac{T}{N}\right)\right] where \hat{I}, \hat{M(j)} are matrices. My problem is that Mathematica interprets this product as element-wise with respect to the matrices, but I of course want it to use matrix...

Homework Statement Show that (AB)C=A(BC) I am just trying to do this to try to gain some experience with problems like this. I saw in my text that they did a similar example for distributivity using the definition of matrix multiplication, so I thought I could use that approach. The Attempt...

Hello, Can we write a summation of exponentials, as a multiplication of exponentials? Regards

Hi, I want to multiply two lists of the format {a1,b1,c1...}*{a2,b2,c2...} to obtain the list {a1*a2,b1*b2,c1*c2,...}. I tried using . to multiply the two lists but that didn't work. What command do I have to use to obtain the desired result? Thanks

I searched around a while on the site to see if I could find a thread that could answer this question and was unable to find one. If this has already been asked before, I apologize. I'm having a problem with something in the AES crypto algorithm...

multiplication and addition principle for count possibilities??/ we toss a fair coin 5 times and recored the sequence of head and tails obtained.how may sequences are possible that start with head OR end with head.? so what i did was using addition theorm i divided this complex process...

Hi. I'm trying to find the degree of the map of f(g,h)=g.h (i.e. multiplication in g) for fixed g. It is a map G-->G (if we fix g). We can assign a degree to this map for any topological group for which the last non-zero homology group is Z and proceed like we do for the degree of a map...

Hihi, Let's say I have the linear equations ,A 2x +3y +4z 5x+6y-7z 5x-4y+3z then I can always write as a matrix multiplication A= B*x matrix B = 2 3 4 5 6 -7 5 -4 3 times matrix x x y z Then., how can I tell MATLAB to express in the matrix multiplication form so...

Theorem 2.15: Let A be an m x n matrix with entries from F. Then the left-multiplication transformation L_A: F^n --> F^m. Furthermore, if B is any other m x n matrix ( with entries from F ) and B and D are the standard ordered bases for F^n and F^m, respectively, then we have the following...

Homework Statement Actually i want to ask something actually very easy... i just don't know the meaning of some words in different questions... firstly... multiplication of A and B means A*B right? how about multiplication of A by B means A*B or A/B?? secondly... division of A by B means...

This is a simple question from Groups and their Graphs by Grossman and Magnus that I just can't figure out: Consider the set {1, 2, 3,..., p-1} where p is a prime number, with binary operation "multiplication modulo p." Show that for any element x of the set there is an element y of the set...

What would be the proof for matrix multiplication?...or just an explanation as to why its done the way its done.

I am reading (theorem 2.14) from a textbook, and don't understand how g = Tf and (#1) line of reasoning. The theorem and proof is as follows: Theorem 2.14: Let V and W be finite-dimensional vector spaces having ordered bases B and C, respectively, and let T: V-->W be linear. Then, for...

Can anyone explain why \frac{-1}{x_0^2} (x - x_0) = \frac{-x}{x_0^2} + \frac{1}{x_0}? Is \frac{-1}{x_0^2} (x - x_0) = \frac{-1}{x_0^2} . \frac{(x - x_0)}{1}? After that I multiply to get \frac{-1}{x_0^2} (x - x_0) = \frac{-x + x_0}{x_0^2} = \frac{-x}{x_0^2} + \frac{x_0}{x_0^2}. Then divide...

how to present this matrix as a multiplication of elementary matrices \bigl(\begin{smallmatrix} 0 &6 &2 \\ 1& 1 &0 \\ 5&3 &1 \end{smallmatrix}\bigr) i can't understand in general what are they doing in this solution http://img144.imageshack.us/img144/9508/34036247.th.gif ??

Hello, Can an integer always be represented through the multiplication of two or more integers? (Are all integers divisible by some set of 2 or more integers (- or +)?) For example, 8 is can be represented by 1 x 8, 2 x 4 and 2 x 2 x 2. But what about 257 or even - integers? I'm trying...

I'm having problems wrapping my head around this...so I want to post some questions out of this Introductory Combinatorics book and what I believe to be the solutions: 1.) There are 6 rooks placed on a 6 by 6 chessboard. How many ways if there are 2 red and 4 blue? I got 6!*\binom{6}{4}...

Given a subset W of a vector space V = F^n (for some field F), prove that W is the subspace of solutions of the matrix equation AX = 0 for some A.

Homework Statement Establish associative law of multiplication by considering absolute values and arguements. z1(z2z3)=(z1z2)z3 Homework Equations The Attempt at a Solution I think I need to use r(costheta +isintheta)...

Where A = a 2*2 matrix, is the following true: (A^n)(A^m) = (A^m)(A^n) Thanks in advance

Homework Statement Show that A and Inverse(I+A) commute (where I is the identity matrix). Homework Equations Inverse(Inverse(A))=A Inverse(AB)=Inverse(B)*Inverse(A) The Attempt at a Solution My solution assumes the existence of the inverse of A. A*Inverse(I+A) =...

Matrix multiplication: Commutative property. Hello, First time poster. I have got a question about commutative property of matrix multiplication. Literature says that matrix multiplication is communicative only when the two matrices are diagonal. But, I have a situation with an...

I'm not sure where to put this question, since it deals with both physics and math, so I figured here would be a good starting point. In the book of astrodynamics I'm currently reading, I came across this expansion...

i have vector "a" why a*a=1?? it make no sense the formula says |a|*|a|*cos0=a^2 (not 1)

i am given two matrices 4X4 which i need to multiply by one another but in my calculator i can multiply matrices only 3X3 how can i use this maximum 3X3 matrices multiplication in order to calculate the multiplication of two 4X4 matrices ?? (i know how to multiply matrices in theory...

i am given two matrices 4X4 which i need to multiply by one another but in my calculator i can multiply matrices only 3X3 how can i use this maximum 3X3 matrices multiplication in order to calculate the multiplication of two 4X4 matrices ?? (i know how to multiply matrices in...

Homework Statement construct a multiplication table for the ring Z_{3}[\alpha], \alpha^{2} + 1(bar) = 0(bar) Homework Equations The Attempt at a Solution I'm actually confused on how to find the elements of the ring. My book and notes have thrown me off a bit and I can't find...

I was wondering what owuld the outcome be if I multiply both normal distribution eg N (5, 100 ) and M ( 10,100 ) i know the operations for addition and subtraction but what if N.M what do i get ?

This is for 10th root unity with complex number multiplication. I am working on closure. I have multiplied 2 elements of my set and I have so far that cos[(n+k)360/10] + isin[(n+k)360/10]. Thus I know that if n+k<=9 then there is an element in the set. Now I need to show for if n+k>9 and if...

Homework Statement In the product (Vector F) = q(Vector v) X (Vector B), take q = 2, (Vector v) = 2.0i + 4.0j + 6.0k (Vector F) = 4.0i - 20j + 12k What than is (Vector B) in unit-vector notation if Bx = By Homework Equations dot and cross products The Attempt at a Solution...

Homework Statement Prove the formula. Homework Equations Matrix multiplication: (\text{AB})_{i \,j}=\sum _{k=1}^n a_{i \,k}b_{k \,j} The Attempt at a Solution I do not know how to "prove" the formula for arbitrary values of k and n.

A set S of (necessarily square) matrices is said to be closed under multiplication if AB∈ S whenever A, B ∈ S. Which of these matrices are closed under multiplication? Circulant matrices Upper triangular matrices Hessenberg matrices My trouble: How do I go about figuring this one out?

Hi to everyone, i'm writing a program in C that is supposed to run on a AVR processor with registers and int of 16 bit (like the one used in some sensor for WSN). This program involves the use of the Lagrange Interpolation. I've worked on it managing to solve most part of the problems but I'm...

I have the following problem: find the first 3 non-zero terms in the Maclaurin series for the function: e-x2 + Cos[x] I know in this case, the series behave like polynomials and I have done the following. The left expression is the first 3 terms of the e portion of the problem, and the...

Homework Statement Prove the following theorem: A(BC)=(AB)C. Homework Equations http://en.wikipedia.org/wiki/Matrix_multiplication#Ordinary_matrix_product" The Attempt at a Solution Let A be of order m by n, B be of order n by p, and C be of order p by q. Then...

Geometrically, matrix multiplication of an nxn matrix is the scaling, and rotation of a vector in n dimensions true? So when you find the inverse of a matrix, what you're actually doing is finding a transformation such that in the 'transformed space' the vector is a unit vector. If the inverse...

How do we define multiplication i mean..like if we have sqrt3*sqrt2 We can't say it is adding sqrt3 sqrt2 times... so wat is multiplication exactly thanks

Can somebody please explain effective neutron multiplication factor, with example? So when k=1, k>1, k<1 , please give me some example. k=\frac{N_2}{N_1}=\frac{N_3}{N_2}=...=\frac{N_i}{N_i_-_1}

Homework Statement I can't figure out how to latexa 3X3 matrix so here's my ghetto method A = 0 0 -1 0 2 0 0 0 1 What is Homework Equations I'm trying to find A^{7} The Attempt at a Solution I'm assuming there's some type of shortcut to get...