Matrix Definition and 1000 Threads

Homework Statement Hi all! I'm having trouble understanding the implementation of some derivatives in the expression (1) of this article: https://www.ncbi.nlm.nih.gov/pubmed/26248210 How do I implement ∑(ij) ∂ijw ? Thank you all in advance. Homework Equations w is a square matrix(120x120)...

Homework Statement Consider an ensemble of spin 1 systems (a mixed state made of the spin 1 system). The density matrix is now a 3x3 matrix. How many independent parameters are needed to characterize the density matrix? What must we know in addition to Sx, Sy and Sz to characterize the mixed...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of Bresar's Example 1.10 on a simple matrix ring over a division ring ... Example 1.10, including some...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of Bresar's Example 1.10 on a simple matrix ring over a division ring ... Example 1.10...

$A=\begin{bmatrix} 3&2\\ \end{bmatrix} B=\begin{bmatrix} 1\\ 2\end{bmatrix}$ Find the value of the matrix $AB$. The order of the first matrix is 1*2 The order of the second matrix is 2*1 Matrix AB should be 1*1 I am a bit struggling in determining the way...

I am facing some difficulties solving one of the questions we had in our previous exam. I am sorry for the bad translation , I hope this is clear. In each section, find all approppriate matrices 2x2 (if exists) , which implementing the given conditions: is an eigenvector of A with eigenvalue...

Hello everyone, I'have implemented a Maximum-Likelihood-Expectation-Maximization Algorithm in order to reconstruct a bild. let say, we have such a system Ax=b, where A is a complex matrix, b is a complex vector. A and b are known and we will iterately try to find the best x (which should be...

Homework Statement Homework Equations determinant is the product of the eigenvalues... so -1.1*2.3 = -2.53 det(a−1) = 1 / det(A), = (1/-2.53) =-.3952 The Attempt at a Solution If it's asking for a quality of its inverse, it must be invertible. I did what I showed above, but my answer was...

I have a Hamiltonian represented by a penta-diagonal matrix The first bands are directly adjascent to the diagonals. The other two bands are N places above and below the diagonal. Can anyone recommend an efficient algorithm or routine for finding the eigenvalues and eigenvectors?

Hello all Let ##m_A: \mathbb{K^n} \rightarrow \mathbb{K^n}: X \mapsto AX## and ##A \in M_{m,n}(\mathbb{K})## (I already proved that this function is linear) I want to prove that: A regular matrix ##\iff m_A## is an isomorphism. So, here is my approach. Can someone verify whether this is...

Hey! :o We have that a matrix $A$ is idempotent if it holds that $A^2=A$. We suppose that $X$ is a $m\times n$-matrix and that $(X^TX)^{-1}$ exists. I want to show that $A=I_m-X(X^TX)^{-1}X^T$ is idempotent. I have done the following: $$A^2 =A\cdot A=(I_m-X(X^TX)^{-1}X^T)\cdot...

Hello everybody, From a complete set of orthogonal basis vector ##|i\rangle## ##\in## Hilbert space (##i## = ##1## to ##n##), I construct and obtain a nondiagonal Hamiltonian matrix $$ \left( \begin{array}{cccccc} \langle1|H|1\rangle & \langle1|H|2\rangle & . &. &.& \langle1|H|n\rangle \\...

Homework Statement Find out for which values of ##\alpha## the system ##AX + \alpha X = (1, 1, 1, 1)^t## has solutions. $$A = \begin{pmatrix} 6 & 0 & -1 & 2 \\ 3 & 5 & -3 & 6 \\ -2 & 0 & 7 & -4 \\ 2 & 0 & 1 & 0 \end{pmatrix} X = \begin{pmatrix} x \\ y \\ z \\ t \end{pmatrix}$$ Homework...

Is there any way that i can convert a non-hermitian matrix to a hermitian matrix ?

Homework Statement [/B] Homework Equations N/A The Attempt at a Solution What I am confused about is where they got the (1/4)mR^2 + (1/12)ml^2 and (1/2)mR^2 from? I am guessing that these came from the integral of y'^2 + z'^2 and x'^2 +y'^2 but I don't understand how this happened exactly...

Homework Statement Consider a quantum mechanical system with three states. At each step a particular particle transitions from one state to a different state. Empirical data show that if the particle is in State 1, then it is 7 times more likely to go to State 2 at the next step than to State...

Homework Statement Consider the following matrix. A = 2 + 4i...1 + 5i 2 − 3i...2 + 3i Let B = A-1. Find b12 (i.e., find the entry in row 1, column 2 of A−1) Homework Equations A-1 = 1/(ad - cb)* [ d -b ] [ -c a ] <--imagine as 2x2 matrix with first row (d,-b) and second row...

Say, I have a matrix which I obtained from a website for matrix calculation, how to insert it into an excel so as for each cell in the matrix, there is a corresponding cell in the excel sheet?

Homework Statement How to calculate the matrix elements of the quantum harmonic oscillator Hamiltonian with perturbation to potential of -2cos(\pi x) The attempt at a solution H=H_o +H' so H=\frac{p^2}{2m}+\frac{1}{2} m \omega x^2-2cos(\pi x) I know how to find the matrix of the normal...

Hello! I need to find the rotation matrix around a given vector v=(a,b,c), by and angle ##\theta##. I can find an orthonormal basis of the plane perpendicular to v but how can I compute the matrix from this? I think I can do it by brute force, rewriting the orthonormal basis rotated by...

Homework Statement For what ##h## is the matrix ##\begin{bmatrix}1 & -h^2 & 2h \\ 0 & 2h & h \\ 0 & 0 & h^2 \end{bmatrix}## diagonalizable with real eigenvalues? (More than one may be correct) a) -2, b) -1, c) 0, d) 1, e) 2 Homework EquationsThe Attempt at a Solution We already know the...

I would love to get help on this problem: Suppose that $M$ is a square $k \times k$ matrix with entries of 1's in the main diagonal and entries of $\frac{1}{k}$ for all others. Show that the rank of $M$ is $k$. I think I should go about by contradiction, that is, by assuming that the column...

Homework Statement If a 3 x 3 matrix A is diagonalizable with eigenvalues -1, and +1, then it is an orthogonal matrix. Homework EquationsThe Attempt at a Solution I feel like this question is false, since the true statement is that if a matrix A is orthogonal, then it has a determinant of +1...

Just a couple of quick questions on index notation, may be because of the way I'm thinking as matrix representation: 1) ##V^{u}B_{kl}=B_{kl}V^{u}## , i.e. you are free to switch the order of objects, I had no idea you could do this, and don't really understand for two reasons...

Homework Statement Suppose that a square matrix ##A## satisfies ##(A - I)^2 = 0##. Find an explicit formula for ##A^{-1}## in terms of ##A## Homework EquationsThe Attempt at a Solution From manipulation we find that ##A^2 - 2A + I = 0## and then ##A(2I - A) = I##. This shows that if we...

Let A be a 4×3 matrix and let c=2a1+a2+a3 (a) If N(A) = {0}, what can you conclude about the solutions to the linear system Ax=c? (b) If N(A) ≠ {0}, how many solutions will the system Ax=c have? Explain.

This might be a dumb question, but I am wondering, given the equation ##A\vec{x} - 7\vec{x} = \vec{0}##, the factorization ##(A - 7I)\vec{x} = \vec{0}## is correct rather than the factorization ##(A - 7)\vec{x} = \vec{0}##. It seems that I can discribute just fine to get the equation we had...

Let the matrix of partial derivatives ##\displaystyle{\frac{\partial y^{j}}{\partial y^{i}}}## be a ##p \times p## matrix, but let the rank of this matrix be less than ##p##. Does this mean that some given element of this matrix, say ##\displaystyle{\frac{\partial y^{1}}{\partial u^{2}}}##, can...

Homework Statement The system is a spring with constant 3k hanging from a ceiling with a mass m attached to it, then attached to that mass another spring with constant 2k and another mass m attached to that. So spring -> mass -> spring ->mass. Find the normal modes and characteristic system...

Hello, I was refreshing my Mathematics using S.M. Blinder's book "Guide to Essential Math" and on the section on Matrix Multiplication I got the following, Can someone elaborate on the highlighted section? In particular, what does "adjacent indices" mean? Thank you.

<< Mentor Note -- thread moved from Homework Help forums to General Math >> Good day, I run coding in Mathematica. But, I get singular matrix A at certain loop. In theory, how can I make matrix A become orthogonal A=\begin{pmatrix} 0& 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0& 0 & 0 & 0 & 0 & 0 & 0 &...

To me it seems basic question or even obvious but as I am not mathematician I would rather like to check. Is it true that these two matrices are both identity matrices: ##\begin{pmatrix}1&0\\0&1\end{pmatrix} ## and...

i don't understand how to get second box using first box in the picthure that has attached.could someone help me?

Hi. When referring to matrices what does ℝm x n mean ? Does this notation also apply to vectors ? Thanks

Extracted from 'At the frontiers of Physics, a handbook of QCD, volume 2', '...in the physical Bjorken ##x##-space formulation, an equivalent definition of PDFs can be given in terms of matrix elements of bi-local operators on the lightcone. The distribution of quark 'a' in a parent 'X'...

Hi, I know the generalized hookes law between stress and strain is given by the elastic tensor. This matrix has 81 constants which are reduced to 9 in the isotropic case. Can someone please help me to understand intuitively how this reduction in the elastic tensor takes place and why some of the...

I am working on this problem which has been baffling me since the beginning: Prove that $A^k = 0$ and $A^{k-1} \neq 0$ if $A_{k \times k}$ is a zero matrix but with entries of 1's right above its diagonal. For example, if $k = 3$ the it will look like this $$\begin{pmatrix} 0 &1 &0\\ 0 &0 &1\\...

Homework Statement Prove that the upper triangular matrices form a subspace of ##\mathbb{M}_{m \times n}## over a field ##\mathbb{F}## Homework EquationsThe Attempt at a Solution We can prove this entrywise. 1) Obviously the zero matrix is an upper triangular matrix, because it satisfies the...

I am confused about a transition matrix as I need to prove that if matrix A is positive, then A^(m+1) is also positive. However, when calculating the (m+1)th transition, I need to put matrix A on the left side of equation (A^m)x=x to write A(A^m)x=x. This to me represents after m times...

this is not a homework question, I just want to make sense of the equation here. Assuming matrix A is diagonal, If A_hat=T'AT where T' is an inverse matrix of T. e^(A_hat*t)=T'e^(At)T which implies, e^(T'AT*t)=T'e^(At)T we know that e^(At) is a linear mapping, therefore if we convert f to...

I am reading Louis Rowen's book, "Ring Theory"(Student Edition) ... I have a problem interpreting Rowen's notation in Section 1.1 Matrix Rings and Idempotents ... The relevant section of Rowen's text reads as follows: In the above text from Rowen, we read the following: " ... ... We obtain a...

I am reading Louis Rowen's book, "Ring Theory" (Student Edition) ... I have a problem interpreting Rowen's notation in Section 1.1 Matrix Rings and Idempotents ... The relevant section of Rowen's text reads as follows: In the above text from Rowen, we read the following: " ... ... We obtain...

Jobs available; https://www.google.com.au/amp/www.cnbc.com/amp/2016/10/07/tech-billionaires-think-we-live-in-the-matrix-and-have-asked-scientists-to-get-us-out.html?client=ms-android-telstra-au&espv=1

Homework Statement I have to find the matrix system of Sx, Sy , and Sz using the given information: 190899[/ATTACH]'] Homework EquationsThe Attempt at a Solution for attempting Sx: Ignoring the ket at the bottom, I would get Sx|+> = +ħ/2[[0,1],[1,0]] but my question here is, does the ket at...

I am working on a two-by-two real matrix $M$, with a linear mapping $F$ that returns the sum of $M$ and its transpose. I need to find out the matrix that is associated with the mapping. To the best of my understanding: $$ M + M^T = \begin{bmatrix} r &s\\ t &u \end{bmatrix} + \begin{bmatrix} r...

Given a n x n matrix whose (i,j)-th entry is i or j, whichever smaller, eg. [1, 1, 1, 1] [1, 2, 2, 2] [1, 2, 3, 3] [1, 2, 3, 4] The determinant of any such matrix is 1. How do I prove this? Tried induction but the assumption would only help me to compute the term for Ann mirror.

This sounds like a common application, but I didn't find a discussion of it. Simple case: I have 30 experimental values, and I have the full covariance matrix for the measurements (they are correlated). I am now interested in the sum of the first 5 measured values, the sum of the following 5...

Homework Statement We're given some linear transformations, and asked what the null space, column space and row space of the matrix representations tell us Homework EquationsThe Attempt at a Solution I know what information the column space and null space contain, but what does the row space of...

Suppose that I have an overdetermined equation system in matrix form: Ax = b Where x and b are column vectors, and A has the same number of rows as b, and x has less rows than both. The least-squares method could be used here to obtain the best possible approximative solution. Let's call this...

We know that Poincare matrix which is 0 Kx Ky Kz ( -Kx 0 Jz -Jy ) describes the boost and rotation is very similar to -Ky -Jz 0 Jx...