Multiplication Definition and 496 Threads

1) If A = [aij] is an n x n matrix, the trace of A, Tr(A), is defined as the sum of all elements on the main diagonal of A, Tr(A) = the sum of (aii) from i=1 to n. Show each of the following: a) Tr(cA) = cTr(A), where c is a real number b) Tr(A+B) = Tr(A) + Tr(B) c) Tr(A(Transpose)) = Tr(A)...

Homework Statement Explicitly show, using numbers, that in general NxN matrix multiplication is not commutative. Show this for all N > 1. If I make a matrix A, 2x2, 1 2 3 4 and multiply by matrix B, also 2x2 5 6 7 8 I get AB =/=BA If I multiply a new matrix A, 3x3, 1...

Homework Statement hey guys... i try to do multiplication of two's complement number. I'm using straightforward method, which give me wrong answer.. i know i can't use this method.. but.. i just want to know why.. why i can't use this method? The Attempt at a Solution 1001 x 0101 = 0101101...

Why do we use significant figures in calculations instead of the rate of Uncertainty? (2,5\pm0,4000)*4,000=(10\pm1,6). The number 2,5 has 2 significant figures, which is the same as we will write in the answer, while it should be only one significant figure in the answer if we take the rate of...

I was surprised that I have never had to do this in so long and forgot the basic way to factor out a scalar multiple when a matrix is raised to a certain power (for example -1 for inverse matrices). Basically, I just want some confirmation: (λT)^n= λ^n (T^n ) ∶ for λ ϵ F and Tϵ L(V)...

I can't figure out what an author means by this expression: \textbf{n} \cdot \textbf{e} \cdot (\textbf{I} - \textbf{nn}) and \left(\textbf{u} - \textbf{U}\right) \cdot (\textbf{I} - \textbf{nn}) Here, all I know is that \textbf{u} and \textbf{U} are vectors of length 3. \textbf{n} is a...

Hi, I'm having some trouble solving one of the problems from my homework assignment. Homework Statement Prove: P((AB)C) = P(A(BC)) Where A,B,C are either true or false. Homework Equations We can't do this by using a truth table, we can use the following equations: P(A + B) = P(A) + P(B) -...

Help me Understand "Closed Under Addition" and "Closed Under Multiplication" Linear Algebra...matrices...etc Examples would be great. Thanks.

Hi! Could anybody, please, tell me: whether |Cos(theta)|*Cos(theta) = Cos^(theta) , because it means that only positive values of Cos(theta) are taken. Am I right?:shy:

This is supposed to be a proof of trigonometric multiplication of complex numbers: What happened at the =...= point? I understand everything up to that.

Hi, I wonder if anyone knows of a mathematically established way of writing elementwise multiplication between two vectors? In MATLAB you can write A .* B to indicate that you want to multiply the vectors A and B elementwise. In my case, I have two column vectors, A and B, and I want to...

Homework Statement If OA = 1/3OB + 2/3OC, then prove that A, B, and C are collinear and that A divides the segment BC in the ratio 2:1. Homework Equations OA = 1/3 OB + 2/3OC A divides segment BC into 2/3s The Attempt at a Solution I don't know where to start on this...

Homework Statement Determine whether or not W is a subset of R4 W is the set of all vectors in R4 such that x1x2=x3x4 Homework Equations Two methods. u+v (addition) cu (multiplication) The Attempt at a Solution I having trouble getting the hang of subspaces. I thought I was getting close...

Hi everyone, I have trouble depicting the difference between these two problems. The first problem uses the multiplication rule to solve while the second problem uses the counting rules (combination) to solve. To me, it seems like both problems could be solved using the multiplication rule so I...

I am having a difficult time grasping the multiplication rules - The rules are easy to remember but actually applying it to a problem is so confusing and frustrating as I don't know whether to use Rule #1 (independent events) or Rule #2 (Dependent events). Here's a problem from my book that I...

Hello everyone, I have a list, let's call it L1, of length N. Each element of this list is a square matrix. I would like to : 1/ Apply MatrixExp[] to each element of L1 (I know how to do that) 2/ Multiply each element of the subsequent list _in an ordred fashion_ i.e. from element N to...

Homework Statement so.. let the operation * be defined as x*y = x + y + xy for every x,y ∈ S, where S = {x ∈ R : x ≠ -1}. Now i have proven associativity, existence of an identity and inverses, all without commutativity, but i must show that this is an abelian group, so now i have to show...

Here is my question(It is not a homework problem.) What does it mean to multiply two matrices? I know how to do the operation but what is the concept behind it? I understand dot products and vectors. Matrix multiplication can be seen as a dot product operation of row vector of vector A to...

Homework Statement A is an mxn matrix and C is a 1xm matrix. Prove that CA=Sum of (C sub j)*(A sub j) from j=1 to m. Where A sub j is the jth row of A Sorry for the messy problem statement, I couldn't figure out the summation notation on here. Homework Equations The Attempt at a...

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...

I'd like to type a few tables similar to the one below into a LaTeX document. \begin{tabular}{c|cc} $\cdot$ & 1 & -1 \\ \hline 1 & 1 & -1 \\ -1 & -1 & 1 \\ \end{tabular} It comes out much smaller than this in my LaTeX document. Is there an easy way to make it bigger? Also, it appears on...

Can we multiply a row with a variable and add it with another row while solving homogeneous system of equations as a matrix?

Hi, thank you for viewing this thread. My question is as follow: Suppose A is a n x m matrix and B is a m x n matrix, and we also know that the matrix B has infinite solutions, then what will the solution/s of the matix product AB be? I am thinking that it might be a matrix of infinite...

Hello I am using Landau's mechanics Vol I for classical mechanics. On page 4 he mentions for Lagrangian of a system composed of two systems A and B which are so far away so that their interactions can be neglected. then for the combined system we have L = LA + LB I'm trying to...

Hi, I am having an issue with multiplication in C++. I am writing a program to check the validity of an NHS number. To do this I must; multiply digit 1 of the NHS number by 10, multiply digit 2 of the NHS number by 9, multiply digit 3 of the NHS number by 8 ...etc The answer from each...

Say you have two functions, F(x,y), and G(x,y), and you want to expand them in finite Fourier series. Let their coefficients be designated as F_ij and G_ij. When you multiply the two functions, you get X=FG, and this should also have its own Fourier series, call its components X_mn. What is the...

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...

All right, I've been doing a lot of reading on quaternions, and while I think I understand how to use them, I'm still very confused as to why certain things are defined the way that they are. First question: Why, when multiplying the imaginary portions of quaternions do you get these "rules"...

Hey, When trying to multiply the 2 attached matrixes (row X column) I get a much more terms then the attached answer. C is for cos and s for sin. What am I doing wrong? Regards, i.l

Homework Statement Find the Laplace transform of the given function, a and b are real constants. Hint: cos(bt)=(e^ibt+e^-ibt)/2 and sin(bt)=(e^it-e^ibt)/2i. f(t)=e^(at)*sin(bt) The attempt at a solution The LaPlace transform of e^at is 1/(s-a). The LaPlace transform of sin(bt) is...

Homework Statement Create a multiplication table for the group of invertible elements in the ring Z_{10}. Can you rename the elements and arrange them so that the multiplication table is transformed into a multiplication table for the group Z_n for some n? Homework Equations The Attempt at a...

This isn't exactly a homework problem I just want to clarify things for myself. I am looking back at my algebra notes and I am seeing cosets and factor groups in a new way. If N is a normal subgroup of G, then the set of left cosets of N forms a group under the coset multiplication given...

Homework Statement Consider this group of six matrices: Let G = {I, A, B, C, D, K}, Matrix Multiplication> I =\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix} A =\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix} B =\begin{bmatrix}0 & 1\\-1 & -1\end{bmatrix} C =\begin{bmatrix}-1 & -1\\0 &...

it is given that e^jwt=cos(wt)+jsin(wt)... but j=1 with angle 90 degrees..now by multiplying any function by j means multiplying the magnitude by 1 and phase change of 90 degree... so, jsin(wt)=sin(wt)*1 with angle 90 degrees = sin(wt+90) =cos(wt)...

Homework Statement Suppose that the power series \Sigma[a]_{n}[/tex]z^{n} and \Sigma b_{n} z^{n} havr radii of convergence R! and R2 respictively. Prove that the radius of convergence of the multiplication is at least R1 * R2 Homework Equations The Attempt at a Solution I...

Homework Statement I've already figured out the code for part 1 of the assignment. I'm stuck on part 2. Specifically, I'm not sure how one would obtain the values for the multiplier and multiplicand from R6, as the notes from the professor in the code claim, nor how to format the result in...

Hello, The map \psi \mapsto A \psi for \psi \in L^2 , where A is a function and A \psi represents pointwise multiplication, is a bounded map on L^2 if A is essentially bounded. However, the map is not necessarily Hilbert-Schmidt, as for example the identity map (corresponding to...

Can anyone tell me what's the formula for even and odd number multiplication. For example, what would be the product for 2 x 4 x 6 x 8 x 10 ... x 100 and what would be the product for 1 x 3 x 5 x 7 x 9 x 12 ... x 99? I am trying to solve a problem which asks me to prove that 1/2 x 3/4 x 5/6 ...

When two bodies interact 'multilication' sign is mostly (always) used. It is used in various other instances also. Why not 'addition' sign? ( I know that multiplication can be understood as continued addition). Some technical answers please. For example p=mv why not p=m+v

This formula is much easier than the standard 10x-x to do in your head. I have been able to do 3 digit numbers with this trick easily, and I'm generally not that great at doing math in my head. Anyway, he it is: http://dratsab.deviantart.com/art/Multiplication-of-9-s-Trick-85433340

if A is [A1|A2|A3|...|An] and C is 1 column matrix given by [C1|C2|C3|...|Cn]T then AC=C1A1+C2A2+...+CnAn.. If D is a diagonal matrix then AD = [D11A1+D22A2+...+DNnAn]. please explain why it happens tht way and whts the prof?

| 1 1 1 | = matrix A | 1 2 3 | | 1 4 5 | How do I find a 3x3 matrix B, excluding the identity or zero matrix, such that AB = BA?

What will happen if we multiply infinity with zero? how to describe this situation?

Homework Statement T(n)=b n<=2 8T(n/2)+e(n^(2)) n>2 Homework Equations The Attempt at a Solution O((n^log)2^(7))

Homework Statement A is an nxn matrix. Suppose A has the form (^{U}_{W}^{V}_{X}) in which U, V, W, X are n1xn1, n1x n2, n2xn1 and n2xn2 matrices respectively, such that n1 + n2 = n. If V=0, show that detA = detUdetX Homework Equations detA := \sum _{\rho\in sym(n)} sign (\rho)\Pi ai...

Homework Statement Suppose that A is an n x n matrix such that A(Transpose)A=I. Let x be any vector in R^n. Show that llAxll=llxll; that is, multiplication of x by A produces a vector Ax having the same length as x. Homework Equations Sqrt(x(transpose)x)=llxll The Attempt at a...

Show the progression (6k +1) (k is an integer) is closed under multiplication: Firstly I should check that I remember what this means... If it is closed when you multiply any 2 elements together you get an element that is in the set? So for this I thought just show (6k+1)(6n+1), where k...

It may seem like a very simple question, but I just want to clarify something: Is tensor field multiplication non-commutative in general? For example, if I have two tensors A_{ij}, B_k^\ell then in general, is it true that A_{ij} B_k^\ell \neq B_k^\ell A_{ij} I remember them being...

Homework Statement I'm doing a proof in which I need to show: given that AX = 0, AVX=0 where V is invertible. Also, given that AVY = 0, then AY = 0. Homework Equations The Attempt at a Solution I can't remember from the previous course I took how to do this. I know that I can...

how is the image recognised after electron multiplication (by secondary emission) in a Micro channel plate in the intensifier of ICCD