Multiplication Definition and 496 Threads

Question: Let n be a positive integer and consider x,y,z to be elements of Zn. Prove that if x . y = 1 and x . z = 1, then y = z. (Since working in Zn the sign '.' means "multiplication modulo n".) Conclude that if x has an inverse element in Zn, then the inverse element is unique. Attempt...

Homework Statement This isn't homework, but I didn't know where else to ask and I have a test in an hour and a half. The study guide says be able to explain why statements like (A+B)^2 = A^2 + 2AB + B^2 are bogus when dealing with matrix's. Is it because (A+B) = (B+A) but (A+B)^2 /= (B+A)^2 or...

say i have some vector ##\vec{v}## multiplied by a scalar k. the norm of ##\vec{v}## would be just ##||\vec{v}||## and the norm of ##k\vec{v}## is claimed to be ##|k|||\vec{v}||## ie, ##||k\vec{v}||=|k|||\vec{v}||## ie the sign of the constant is irrelevant. when i work it out...

I'm trying to figure out if ##\mathbb{R}/k\mathbb{Z}## would form a field if we allowed for an "induced" multiplication from ##\mathbb{R}##, with ##r\in\mathbb{R}/k\mathbb{Z}## identified with ##r+k\in\mathbb{R}/k\mathbb{Z}##. So, if we wanted to multiply ##3\in\mathbb{R}/4\mathbb{Z}## by...

The problem given says to consider the addition and multiplication \(\oplus\) and \(\odot\) on \(\mathbb{Z}_6\) defined by $$[m]\oplus[n]=[m+n]$$ and $$[m]\odot[n]=[mn].$$I need to verify, among other things, that the multiplication cancellation law fails (if \([m]\odot[j]=[m]\odot[k]\) and...

Is there anyway around this problem? syms m,n; x1 = [0, 1, 4, m]; x2 = [3, n, 9, 27]; conv(x1,x2) Undefined function 'conv2' for input arguments of type 'sym'

Let a positive definite matrix A be factorized to P and Q, A=P*Q and let an arbitrary matrix B. I am calculating the relative error of the factorization through the norm: \epsilon = \left\| \textbf{A}-\textbf{PQ} \right\| / \left\| \textbf{A} \right\| which gives \epsilon <1\text{e}-16 so I...

Homework Statement This isn't actually a homework question but i thought this would be the right place for it... I am doing exam review and this question is giving me difficulties. Consider the 3x3 diagonal[1,3,1] matrix A. Find nonzero vectors x in ℝ^{3} such that ||Ax||_{3} = ||A||_{3}...

Homework Statement A=[1 0 0] [1 0 1] [0 1 0] Find A^50 Homework Equations The Attempt at a Solution I'm sure that we can't multiply it 50 times...it's a tedious process , there must be a short cut

The title says it all. Commutative* sorry Mod note: fixed title.

Instead of i2 = -1, is it useful to think that (-i)i = 1, i.e. opposites cancel each others, kind of doing an addition instead of the multiplication ? If I replace i with "direction" it kind of makes sense. (I like to think that this is not just math but also physics.)

Hello. Can someone show me the step by step method to multiply a 5x5 matrix? Here, I am required to use boolean algebra, so the answer will end up only having 0 and 1.

How does one change the dot product such that there is no dot product in between, just plain multiplication? For example, in the following: eb.\partialcea=-\Gammaa bc How do I get just an expression for \partialcea?

Consider two square matrix A,B each specifying a parallelopiped by three different vector. The x, y, z components are written in column 1, column 2, column 3 respectively. Thus the order of A , B is 3x3. Let C=AB. To get the c11 element of C i do a dot product of row1 of A and column 1 of B...

1111010 x 1001 is a negative * a negative so I should get a positive right? which I got 0001001010. BUT, if it's -122 x -9 = 1098. How come I get a positive number that doesn't equal 1098. Aren't you supposed to disregard the most left bit if it's more numbers than your original like wouldn't...

Hi, Does the author mean that −3 × 4 = 0 − 3 × 4 = −(3 × 4) or else? I consider the minus-sign to be a unary operator, which is preceded by multiplication and division. Am I thinking right?

The problem is: Let A be a real m x n matrix and let x be in R^n and y be in R^m (n and m dimensional real vector spaces, respectively). Show that the dot product of Ax with y equals the dot product of x with A^Ty (A^T is the transpose of A). The way I went about starting this problem is to...

The context in which this question arises (for me), is I was trying to take the curl of the magnetic field of a moving point charge, however my question is purely mathematical. But I will explain the situation anyway. The point charge is located at \vec{r_{0}}, moving with velocity \vec{v}. The...

I have a problem with something that should be very simple,I do not no if it is programming issue or my ignorance. If I have matrix c(5,5) 3 0 0 0 0 1 2 0 0 0 0 1 2 0 0 0 0 1 4 1 0 0 0 1 2 and vector b(1,2,3,4,5) c*b=a a=(3,5,8,24,14) FORTRAN MATMUL C=MATMUL(B,A) Correct?

I was wondering if anybody can see where I have gone wrong here? I was given the rule, E2(E1A1)=(E2E1)A1, I can't seem to find my mistake.

In physics new units are usually multiplication or division of some physical quantities. Why is there no unit which is a result of addiing or subtracting other units? I'm sensing this is a rather stupid question but still I'm going to ask anyway. Thank you!

Mathematics is all around sciences.It is also considered a language.In language everything should have meaning. I know addition and subtraction meaning.Same things[quantities ,etc.] can add or subtract . It cannot be done on different things. What is the meaning of multiplication and...

I am doing linear algebra and want to fully understand it, not just pass the class. I was recently taught matrix multiplication and decided to look up how it works. The good part is that I understand the concept. Matrices are a way of representing linear transformations. So matrix multiplication...

How this is defined? ##\vec{r}\cdot \vec{\sigma}##? where ##\vec{r}=(x,y,z)## and ##\vec{\sigma}=(\sigma_x,\sigma_y,\sigma_z)##. ##\sigma_i## are Pauli spin matrices.

I am looking for a transformation that relates a matrix product with a matrix addition, e.g. AB = PA + QB Is there any such transformation? Thnx

Hi Everyone! I'm with Conditional Probability and I don't understan this theorem. Theorem: If http://imageshack.us/a/img28/1349/1qg.png then http://imageshack.us/a/img209/8829/aor.png Proof: All the conditional probabilities are well defined, since http://imageshack.us/a/img197/8938/4xp.png...

Destiny C Sweet on Facebook writes: Can someone take a look at this mixed number multiplication problem below... and explain to me how they got this answer? When you work the problem out find the product and reduce to the lowest terms... \[4\frac{3}{4}\times 9\frac{4}{8}=45\frac{1}{8}\]

Homework Statement what is 33.3 X 45.1 using significant figures?Homework Equations basic multiplication and significant figures. The Attempt at a Solution I got 1501.83 in my calculator. I'm confused with the original problem because it has 4 digits before the period however you have to...

we all know the basic rules for operations of addition, subtraction, multiplication and division. but what i don't know is why these rules (of addition, subtraction, multiplication and division) works. as if we have been given algorithm to do these operations but not explained how they...

Hi. Write an external function that takes two matrices, multiplies them and returns the resulting matrix. Matrices can be of any dimension. Print the resulting matrix The above is what I have to do. http://paste.servut.us/pgmm This is what I've done so far. But it seems like...

$\dfrac{3}{3\times 4}+\dfrac{4}{3\times 4\times 5}+\dfrac{5}{3\times 4\times 5\times 6}+\cdots+\dfrac {99}{3\times 4\times 5\times 6\times \cdots\times 99\times 100}$

Homework Statement i have an 8 bit input, and i need to represent 0-359 in decimal on 3 7-seg displays The Attempt at a Solution with 8 bits there is only 256 possibilities so the input would have to be multiplied by 1.4 to get an even spread over 259 degrees. but you can't multiply...

Hi guys having a little trouble with two-qubit state multiplication. Could you tell me how you work out the following? (not only the answers but the working out) I need to be able to understand these calculations before I can move on to the next step of an entanglement question. I understand...

Problem Statement We are asked to use the following divide and conquer algorithm to get the solution for the multiplication of some matrix A and some matrix B. (See below) Consider the matrix sizes. Comment the total computational time used on the following three algorithms, when different...

Hey everyone, I'm struggling with the summation notation for matrices and vector operations, multiplication in particular. Please refer to the image below where I've typed it all out in Word, its too cumbersome here and I want my meaning to be clear...

Homework Statement Let M2 denote the set of all 2x2 matrices. We define addition with the standard addition of matrices, but with scalar multiplication given by: k \otimes [a b c d] = [ka b c kd] (note that they are matrices) Where k is a scalar. Which of the...

Hello, I know this question may be absurd or very basic, but I need to know what it means when two variables with different units are being multiplied. I need to know what multiplication is in physics, in order to make sense of formulas (such as momentum, force, energy formulas) without only...

Hi; Is there anyone who knows multi-dimensional array multiplication in fortan ? such as; A(5,5,3,3) * B(5,5,3,3) thanks

Homework Statement Consider the field Q(\sqrt{2}), viewed as a vector space of dimension 2 over Q. Let r + s\sqrt{2} \in Q(\sqrt{2}), and define the multiplication map M_{r+s\sqrt{2}}: Q(\sqrt{2}) → Q(\sqrt{2}) by M_{r+s\sqrt{2}}(\alpha)= (r+s\sqrt{2})*\alpha In other words...

How do you multiply 111x111. Every exemple i ve found on internet is 101x100, 110x101 and it doesn't answer to my question :|. 111x 111= 111+ 111+ 111 ---- Every exemple I've found is like :)) 110+ 101 Which is obviously...

Homework Statement I need to use matrix multiplication of matrices A-D to obtain matrix E. I also need to set a equal to some value that would allow me to perform this multiplication. Homework Equations The matrixes I need to multiply: A = [1, 1; 0, 1] B = [1, 0; 1, 1] C = [a, 0...

Hi PF, I have a serious doubt. In spread spectrum modulation etc we multiply the message signal with PN sequence , so as to spread it in frequency domain, good and I am OK with that. But when explanation comes multiplication becomes XOR ing in most books and articles. How XOR...

Why Denote Group Operation with Multiplication?? When groups are introduced in most abstract algebra texts, the operation is denoted by multiplication or juxtaposition and addition notation is reserved for abelian groups. This seems to cause a lot of unnecessary confusion. Professors often...

I understand the meaning behind Division fundamentally, such as one Magnitude being proportional to another. For example, v=m/s means meters per second. Or as a ratio, it means for every one second there is one meter. What I can't seem to wrap my brain around is the concept of multiplying...

Homework Statement In order to highlight the problem I'm having here I have posted two questions, the answer for the second matches the textbook answer, the first does not. The wording of both questions appears to be the same. Have I gone wrong in the 1st question, or is the book incorrect...

\begin{alignat*}{3} A_{ij}B_{ij} & = & (A_{(ij)} + A_{[ij]})(B_{(ij)} + B_{[ij]})\\ & = & A_{(ij)}B_{(ij)} + A_{(ij)}B_{[ij]} + A_{[ij]}B_{(ij)} + A_{[ij]}B_{[ij]} \end{alignat*} $$ A_{(ij)}B_{[ij]} + A_{[ij]}B_{(ij)} = \frac{1}{2}(A_{ji}B_{ij} - A_{ij}B_{ji}) $$ Can I then say $A_{ji}B_{ij} =...

Hi I'm writing a BigNum library for Javascript and have come up with a multiplication algorithm which I think is pretty efficient (a modification of shift/add), but I don't understand O(log ...) notation, so don't really know how to compare my method with something like the Schönhage–Strassen...

I multiplied two series $\displaystyle \sum_{n=1}^{\infty} (-1)^{n} \frac{1}{n^{\frac{3}{4}}}$ and $\displaystyle \sum_{n=1}^{\infty} (-1)^{n} \frac{1}{n^{\frac{1}{4}}}$. I got $\displaystyle 1 + \frac{1}{2^{\frac{3}{4}}2^{\frac{1}{4}}}+\cdots$ I don't know how to write it with symbols so that...

Throughout mathematics, we see the appearance of pi and e, they are integral to every part of mathematics. could this be because the reason all or at least most mathematical problems arise because of the tension between multiplication and addition (pi and e) itself?. certainly the deepest...

Given that a, b, and c are positive integers solve the following equation. a!b! = a! + b! + c^2 anyone?