Multiplication Definition and 496 Threads

Hello, I wanted to ask if this is a correct move, A and B are matrices, a is a scalar, thank you ! A^{2}\cdot B^{t}-aA=A(A\cdot B^{t}-aI)

Homework Statement Consider the left multiplication L_A:R^4->R^3 corresponding the matrix A: 1 2 -1 3 = 2 2 4 -1 6 = 5 0 1 0 2 = 3 What is the rank of L_A and the Range of L_a? Homework Equations The Attempt at a Solution I have two main problems with this question...

I'm having problems running cblas_dgemm on a matix matrix multiplication. I have the following matricies double * mass = new double[n]; double (* pos)[NDIM] = new double[n][NDIM]; double tempPos[NDIM]; double tempMass[nlocal]; double mass_avg[1]; double pos_avg[NDIM]...

let A_i be an odd integer, s_i be the square of a_i and t_i be the triangular number, (s_i -1)/8. Same for a_j , s_j, t_j, etc. Define Multiplication of n X A_i , etc to be n * s_i - t_j and division to be the reverse of this process. I found that n X A_i X A_j X A_k = n X A_k X A_j X...

This isn't a homework help issue, I just want to know what identity(?) this is. a/b to ab or A^2/B^2 to (A^2)(B^2)

Hello I have a question, I need to tell if there exist A such as: A\cdot \begin{pmatrix} 0\\ 1\\ 4 \end{pmatrix} =\begin{pmatrix} 1\\ 2\\ 3\\ 4 \end{pmatrix} how do you approach this kind of questions ? thanks !

Hello, I want to find a family of functions \phi:\mathbb{R} \rightarrow \mathbb{C} that have the property: \phi(x+y)=\phi(x)\phi(y) where x,y\in \mathbb{R}. I know that any exponential function of the kind \phi(x)=a^x with a\in\mathbb{C} will satisfy this property. Is this the only choice...

Homework Statement Let ej denote the jth unit column that contains a 1 in the jth position and zeros everywhere else. For a general matrix An×n, describe the following products. (a) Aej (c) eTiAej? Homework Equations Rows and Columns of a Product Suppose that A = [aij] is m × p and B =...

How to prove that 3 x 2 = 2 x 3?

Homework Statement Hi guys, I'm trying to prove that matrix inversion is continuous. In other words, I'm trying to show that in a normed vector space the map \varphi: GL(n,R) \to GL(n,R) defined by \varphi(A) = A^{-1} is continuous.Homework Equations The norm that we're working in the...

We have two independent random variables X and Y whose pdfs are given as f(x) and f(y). Now when you multiply X and Y you get a random variable say Z. Now what is the resulting pdf f(z)? I mean how is that related to the pdf of f(x) and f(y)? From what I read it looks like f(z)=f(x) *...

Homework Statement Do the following: (a) find an interval I and functions f, g: I → R such that f and g are both Riemann integrable, but f g is not Riemann integrable. (b) find an interval I and functions f, g: I → R such that f and g are both Riemann integrable, but g ◦ f is not...

Hello, I have read several different sources on this very topic, and the one thing that confused a little was defining it using sigma notation. Could some please explain to be what it means?

Ok, so I know how to do it, that is not the question. The question is, why do I always get them wrong. If there is a problem say 323 * 486 Somewhere in the problem I will mess up, it will always be something different than what I messed up on last time. What am I to do? I am very close to just...

I have a nxn tridiagonal matrix (let's name it A) and i want to find a way to solve Ap, p=1,2,3,...inf, most efficient* (using the structure of my matrix) my first problem is how many calculations do i need for A2, and then how many calculations for the hole Ap ? any help please!*by most...

Sometimes I have seen a dash (-) being used as multiplication sign, usually in connection with units. Does anybody know where this strange custom has it's origin?

Homework Statement Homework Equations Tan θ=A.B/|A|*|B| The Attempt at a Solution A=4i-9j B=9i-6j A.B=-18 Magnitude of A = √97 Magnitude of B = √117 Solve that out using Cos-1 (-18/Sqr97*Sqr117) and I keep getting the wrong answer.

We have known that: lim f(x)g(x) = lim f(x) * lim g(x) Could any conditions or limitations make: lim f(x)g(x) ≠ lim f(x) * lim g(x)?

Homework Statement prove by induction that if A and B are finite sets, A with n elements and B with m elements, then AxB has mn elements Homework Equations AxB is the Cartesian product. AxB={(a,b) such that a is an element of A and b is an element of B} The Attempt at a Solution...

1. Why is the norm of a vector noted by double pipes when it is just the magnitude which is notated by single pipes? 2. Does anyone know where I could find out why matrix multiplication is defined the way it is? I know how to do it, but I do not understand why it is that way. Thank you.

Homework Statement Let A be an nxn matrix, and C be an mxm matrix, and suppose AB = BC. (a) Prove the following by induction: For every n∈ℕ, (A^n)B = B(C^n). What property of matrix multiplication do you need to prove this? Homework Equations The four basic properties of matrix...

u and v are contained in V Lets say the scalar multiplication is defined as: ex. ku=k^2 u or ku = (0,ku2) u=(u1,u2) does this mean that this is also the same for different scalar m? mu=m^2 u or mu = (0,mu2) u=(u1,u2) and does this mean the same for any vector v kv=k^2 v or...

u and v are contained in V Lets say the scalar multiplication is defined as: ex. ku=k^2 u or ku = (0,ku2) u=(u1,u2) does this mean that this is also the same for different scalar m? mu=m^2 u or mu = (0,mu2) u=(u1,u2) and does this mean the same for any...

An example: Both conceptually and computationally it is easier to see that 2.5 * 5.2 = 13 than it is to see 13 / 5.2 = 2.5 In programming too: division loops take more CPU resources than multiplication loops. Why is this?

I realized my biggest problem with math so far is I'm having trouble with basic multiplication, and was wondering what was the best way of learning the basic multiplication tables?

When I was little, I noticed that any even number less than 10 multiplied by 6 ends in itself and leads with one half of itself. Any meaning behind that, or coincidence?

Warning: Semantics battle may ensue, tread lightly So I was wondering the other day, the repeated-addition definition of multiplication only works for integers, for example you cannot use this to calculate the square of e or pi. So is there a rigorous definition for multiplication that is...

Homework Statement n * m = m * n where m, n are natural numbers. Homework Equations I am working from Terrence Tao's class notes and he includes 0 in the natural numbers. m++ stands for m+1. He calls it incrementation and uses it to explain the rules of addition. The Attempt at a...

OK - this one has been argued to death in several different threads, but the answers have been less than satisfactory... so someone provide a reason why I am wrong here: 48 / 2(9 + 3) = 2. Why? Because the distributive property of multiplication means that 2(9+3) = (2*9+2*3). For...

Hi, I have five 6x6 matrices defined on mathematica with some unknowns and I need the final matrix let's say, mf. When I tried to find out mf with Dot[] command, it works but the result won't be so logic. On the other hand, when I tried to do this multiplication with . symbol, there exists a...

Suppose that we have a cross-product of vectors. a × b = c Now suppose that we have an orthogonal matrix M. Is it true that (M a) × (M b) = M c ? My intuition is that here we are moving to another coordinate system and performing a cross product in this new system. I can't find an...

If f(x)=\int_0^\infty g(x) dx and I wanted to multiply the integral by, say, a, what would I multiply the left side by? In other words, ? \times f(x) = a \int_0^\infty g(x) dx Thanks in advance!

Hi, If I have a vector c = [ a , 1 ]T where the element a is a vector. If I multiply c by its transpose: cTc is this defined? How do I calculate the a*a? Matrix multiplication rules would say that a * a is undefined because it is a nx1 matrix multiplied by a nx1 matrix. Or is the...

Homework Statement Its not really homework problem, and you may find it silly because its only multiplication problem, but I cannot get the right answer by multiplying quaternions. Basically this is what i want to show: exp(iψ/2)exp(kθ/2)exp(iф/2) = cos(θ/2)exp(i[ψ+ф]/2) +...

Hi, In the middle of the article about Franciscus Vieta, here: http://en.wikipedia.org/wiki/Franciscus_Vieta I see an infinite product as an expression for Pi: 2 * 2/2^(1/2) * 2/(2+(2^(1/2))^(1/2) * ... I was wondering, how this could be written in compact form using math notation please?

!Euler transform matrix multiplication help! Homework Statement This may be rather simple but i am really struggling to complete a 3 3x3 matrix multiplication. I NEED STEP BY STEP WORKING!. This would really help me I understand the theory. Basically I have three matrices T1= cosψ sin ψ...

In robotics, you have a co-ordinate frame which is at the base & another which is at the next joint. You want to describe the position and orientation of the 2nd frame with respect to the first in terms of position and orientation. For the position, you use a translation matrix. The...

Normally with column vectors, we premultiply rotation matrices if the angles are with respect to fixed axis. Why then do we post multiply if the angles are Euler Angles, angles with respect to the mobile axis?

The operation is called "the cross product." I am wondering if there are any specific characteristics that has led mathematicians to consider it a type of multiplication. After taking abstract algebra, the only conclusion I can come away with is that it more closely resembles traditional...

What is the difference between matrix multiplication and the dot product of two matrices? Is there a difference? If, A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} and B = \begin{pmatrix} e & f \\ g & h \end{pmatrix} then does {\mathbf{A} \cdot...

Hello! I'm currently reading John Lee's books on different kinds of manifolds and three questions has appeared. In 'Introduction to Smooth Manifolds' Lee writes that a tensor of rank 2 always can be decomposed into a symmetric and an antisymmetric tensor: A = Sym(A) + Alt(A). We define a...

Dear members, I have a rather silly question. As we all know only the compatible matrices can be multiplied. My derivation of some Finite Element formulation has, however, led me to the multiplication of two incompatible matrices. I was wondering if we could make these incompatible...

Homework Statement I am more trying to figure out how to solve generally rather than solve this specific problem. Nevertheless this problem could be given as: Solve the matrix for A and B. Homework Equations \begin{pmatrix} 1 & 1 \\ 0 & 0 \\ 0 & 2 \\ 2 & 0 \\ 0 & 0 \\...

Homework Statement Hi All, I have a problem in calculating the thickness of a coating material inside a tube. The tubes inside diameter is measured before and after coating. The coating thickness is calculated by substracting the diameters and dividing by two to get the thickness of the...

This was a question for a test of mine. I am unsure how to translate the object from the left image(Fig.1) to the right (Fig.2). I am to use matrix multiplication.. Do i start with the vertices in Fig.1 as a matrix, as in |0 -1 -2 0 -2 -1 | ...............|0 0 0 2 2 3 | (I...

Homework Statement true or false .. The system {S,+,.} with S = { matrix (a,b,a-b,a)|a,b ∊ R) is not a field under matrix addition (+) and matrix multiplication (.) i find that the statement is false . since : 1. {S,+} is Abelian group. 2. {S,.} : is Abelian group. is...

Homework Statement Its a 3x2 multiplying a 2x2. (3 down 2 across, 3x2) I was gone for the day that my teacher explained it to us, and I am not sure how to do it. I tried, but I want to be sure. Homework Equations 5 2 0 -4 _X_ 3 7 1 6 ___ -2 0The Attempt at a Solution The answer I got was...

Hi everyone, I have a problem with finding the transfer function of a linear system. It happens that in some terms the input and the output are multiplying and I have no idea how to do the Laplace transform of this. The system is a car and I am only studying its speed. The input is the...

I'm researching a problem relatived to group SO(8). I have searched many book of theory Group but I did'n find SO(8) isomorphic with what unitary group or their multiplication (SU(n), U(n) or SU(m)*U(n)). Please help me!

Please read the following carefully. The point of the following is to distinguish between T^{\mu}_{\mbox{ } \nu} and T_{\mbox{ }\mu}^{\nu} which clearly involves a metric tensor. But when you want to go from component manipulation to matrix operations you have to be careful. Components are...