Matrix Definition and 1000 Threads

Homework Statement Then solve these equations for i1-4 Homework Equations V=IR The Attempt at a Solution 80i_1-50i_2-30i_3 = -120 -50i_1+100i_2-10i_3-25i_4 = 0. -30i_1-10i_2+65i_3-20i_4 = 0. -25i_2-20i_3+100i_4 = 0. i_1=-4.18239492 i_2=-2.66455194 i_3=-2.71213323 i_4=-1.20856463...

Homework Statement Let ##A## be a 2x3 matrix. If Nul(##A##) is a line through the origin in ℝ3, then Col(##A##) = ℝ2. Explain why. Hint: Think about the number of pivots in ##A##. Homework EquationsThe Attempt at a Solution So, Nul(##A##) is the set of all solutions to the equation ##Ax=0##...

Homework Statement Coupled Harmonic Oscillators. In this series of exercises you are asked to generalize the material on harmonic oscillators in Section 6.2 to the case where the oscillators are coupled. Suppose there are two masses m1 and m2 attached to springs and walls as shown in Figure...

Homework Statement Solve the following coupled differential equations by finding the eigenvectors and eigenvalues of the matrix and using it to calculate the matrix exponent: $$\frac{df}{dz}=i\delta f(z)+i\kappa b(z)$$ $$\frac{db}{dz}=-i\delta b(z)-i\kappa f(z)$$ In matrix form...

We have ##B=(1, X, X^2, X^3)## as a base of ##R3 [X]## and we have the endomorphisms ##d/dX## and ##d^2/dX^2## so that: ##d/dX (P) = P'## and ##d^2/dX^2 (P) = P''##. Calculating the matrix in class, the teacher found the following matrix, call it ##A##: \begin{bmatrix} 0 & 1 & 0 & 0...

Homework Statement Homework EquationsThe Attempt at a Solution I keep getting something over 0 for my Y_11. I'm not sure what I'm doing wrong. I thought the ideal transformer does not have an admittance or impedance matrix, which is why I should be getting something over 0 but the there...

Given that the Hamiltonian is H = P^2/(2m) + aδ(X − x(naught)) + bδ(X + x(naught), where x(naught) is a positive number. Find the conditions for bound states to exist and calculate their energies. Find the scattering matrix for arbitrary values of a and b. Can someone help me solve this please.

<Moved from a homework forum. Template removed.> I can't find any documentation on how to do this. I remember in linear algebra how to find the incidence matrix of an electrical network of purely resistors. Put how do I find it of a RLC circuit with resistors, inductors, and capacitors? I can't...

My teacher told me to find the definition of matrix which is in function form, but haven't seen it. The definition of matrix that I know is a rectangular arrangement of mn numbers, in m rows and n columns and enclosed within a bracket, but it is not right which my teacher wants. I want to know...

I'm trying to get the hang of index gymnastics, but I think I'm confused about the relationship between rank-2 tensor components and their matrix representations. So in Hartle's book Gravity, there's Example 20.7 on p. 428. We're given the following metric: ##g_{AB} = \begin{bmatrix} F & 1 \\...

Hi Lets say I have a txt file with m rows with n columns of numbers of the form: Lets say I want to take every p'th row and take the second and third columns and turn it into a \frac{m}{p}\times 2 matrix. How would I go about doing that?

I want a QM textbook which introduces detail knowledge of density matrix and trace (i.e. the average), who can recommend one for me? Thank you.

Homework Statement given that X is an n × p matrix with linearly independent columns. And $$X^∗ = XA$$ where A is an invertible p × p matrix. a) Show that: $$X^*{({X^*}^TX^*)^-}^1{X^*}^T = X{(X^TX)^-}^1X^T$$ b) Consider two alternative models $$M : Y = Xβ + ε$$ and $$M^∗ : Y = X^∗β ^∗ +...

How we can be sure that we are not living in matrix kind of virtual reality where we even do not have our bodies but all we have is our brain kept in jar of some liquid ? then also how we can be sure that the history as we know it till the last microsecond is totally made up and has been...

SOLVED Hi there. I have the elements of a matrix written in a txt file (in row major order). I need to read this matrix to use it in my fortran77 program. The text file contains the elements written in this way: A(1,1) A(1,2) ... A(1,N) ... A(N,N-1) A(N,N). I was thinking in doing a do loop...

Say we have a matrix L that maps vector components from an unprimed basis to a rotated primed basis according to the rule x'_{i} = L_{ij} x_{j}. x'_i is the ith component in the primed basis and x_{j} the j th component in the original unprimed basis. Now x'_{i} = \overline{e}'_i. \overline{x} =...

Hi All, I am trying to see if there is a "nice" ( relatively straightforward) way of finding the solution/kernel of the map : ##f(A)=A^n -Id ## , where A is an ## k \times k ## matrix and ##n## is a positive integer. Question: what is the kernel of this map? Cranking out matrix coefficients...

Homework Statement Need to prove that the derivative of a rotation matrix is a skew symmetric matrix muktiplied by that rotation matrix. Specifically applying it on the Rodrigues’ formula.Homework EquationsThe Attempt at a Solution I have shown that the cubed of the skew symmetric matrix is...

I want to transform the first matrix below into the second one. The book ( Neutsch, "Coordinates") says this can be done by elementary transformation. I guess he means by some Gaussian elimination. But the entries of the matrix are from the finite field 2, so I can not multiply rows, that would...

Homework Statement Homework Equations Matrix multiplication. The Attempt at a Solution Answer given=4 What am I doing wrong??

Hi, I'm trying to calculate the eigenvectors of a 4x4 matrix, but I don't want the actual eigenvalues included in the solution, I simply want them listed as a variable. For example, I have the matrix: H_F = \left[ \begin{array}{cccc} \hbar\Omega&\hbar v_fk_- &0&0\\ \hbar...

Homework Statement The question asks us to write down the matrix represented by the following summation. 2. Homework Equations The question summation... $$\sum_{j,k=1}^{3} a_{ij}b_{jk}x_{k}$$ The Attempt at a Solution $$ \sum_{j,k=1}^{3} a_{ij}b_{jk}x_{k} =...

It is the demonstration of an important theorem I do not succeed in understanding. "A matrix has rank k if - and only if - it has k rows - and k columns - linearly independent, whilst each one of the remaining rows - and columns - is a linear combination of the k preceding ones". Let's suppose...

Hello Basically i need some help or references on proving that Working with spherical tensors in a 0_ ---> 0+ forbidden beta decay could you please give me some hints on how to do this proof? Thank you

Hey, I want to ask you about the array led component: 1.9mm(0.8’’)8*8 blue dot matrix led displays (model no:KWM-20882XBA). << Edit by Mentor to add link to datasheet >>[/color] https://cdn-shop.adafruit.com/datasheets/956datasheet.pdf I saw the technical data sheet but I couldn’t find the...

Hello. I fail to follow one step in the process of calculating ⟨la∥Y(L)∥lb⟩ . The spherical harmonics Yma(L)(r) represent the 2L+1 components of the spherical tensor of rank L. Writing the Eckart-Wigner th. for M = 0 yields: (1) Also one can write (2) Coupling L and lb to l: (3) Thus...

Homework Statement [/B] The trace of a matrix is defined to be the sum of its diaganol matrix elements. 1. Show that Tr(ΩΛ) = Tr(ΩΛ) 2. Show that Tr(ΩΛθ) = Tr(θΩΛ) = Tr(ΛθΩ) (the permutations are cyclic) my note: the cross here U[+][/+]is supposed to signify the adjoint of the unitary matrix U...

Hi PF! Just want to make sure I'm not crazy: if we're solving a system ##K a = \sigma^2 M a## where ##K## and ##M## are ##n\times n## matrices, ##a## an ##n\times 1## vector and ##\sigma## a scalar, then ##a## is unnecessary, and all we really need to solve is ##K=\sigma^2 M##, right?

Hi. I have a real tridiagonal symmetric matrix that comes from the discretization of a partial differential equation. The elements are given by: ##A_{i,j}=-\delta_{i-1,j}\kappa_{i-1/2,l}\frac{\Delta t}{h^2}+\delta_{i,j}\left[\frac{2}{c}+\frac{\Delta t}{2}\mu_{i,j}+\frac{\Delta...

Hi there. I wanted to ask this question, which is about efficiency in matrix times vector multiplication in fortran. When I have some matrix ##\hat A## and vector ##\vec{x}##, and I want to compute the matrix times vector ##\hat A \vec{x}=\vec{b}## in Fortran, what I do is, I build the array...

Hi, I'm kind of stuck with this theorem stating that: if A is an unipotent matrix, then exp(log A) = A and also if X is nilpotent then log(exp X) = X Does anyone know any good approaches to prove this? I know that for unipotent A, logA will be nilpotent and that for nilpotent X, exp(X)...

I'm trying to construct a Fisher Forecast for the upcoming S4 CMB survey. I don't understand what the C_l is in this formula. It is H(z) and the Angular Distance? Or is it some covariance matrix and if it is a covariance matrix how do I calculate it considering the experiment hasn't been done...

I'm having trouble understanding a step in a proof about bilinear forms Let ## \mathbb{F}:\,\mathbb{R}^{n}\times\mathbb{R}^{n}\to \mathbb{R}## be a bilinear functional. ##x,y\in\mathbb{R}^{n}## ##x=\sum\limits^{n}_{i=0}\,x_{i}e_{i}## ##y=\sum\limits^{n}_{j=0}\;y_{j}e_{j}##...

Homework Statement Prove that a 2x2 complex matrix ##A=\begin{bmatrix} a & b \\ c & d\end{bmatrix}## is positive if and only if (i) ##A=A*##. and (ii) ##a, d## and ##\left| A \right| = ad-bc## Homework Equations N/A The Attempt at a Solution I got stuck at the first part. if ##A## is positive...

We use A = I.A as equation and then by transforming only A of LHS and I of RHS we come to I = P.A and we say that P is the inverse of matrix A My question is that why we only tranform A and I, why A of RHS is left as it is during the transformation, or why transformation do not take place in...

Homework Statement Find the transition matrix ##P## of a transformation defined as ##T:ℝ_2→ℝ_3## ##T:\begin{bmatrix}a\\b\end{bmatrix} = \begin{bmatrix}a+2b\\-a\\b\end{bmatrix}## For basis ##B=\begin{bmatrix}1\\2\end{bmatrix},\begin{bmatrix}3\\-1\end{bmatrix}##...

As we know that 2×3 = 2+2+2 = 6; so similarly what does matrix multiplication represents?

The Internet is full of different communities, one such community is the 'Glitch in the Matrix' community, it is a big community and even has its own reddit page. People here discuss glitches they have experienced during the day, hundreds of people post everyday. Some posts are things that would...

Hello everyone. Iam working on a course in multivariable control theory and I stumbled over the Identity Matrix. I understand what the identity matrix is, though the use of it is a mistery... I was reading about going from state space to transfer functions and I found this expressions...

Homework Statement About an endomorphism ##A## over ##\mathbb{C^{11}}## the next things are know. $$dim\, ker\,A^{3}=10,\quad dim\, kerA^{2}=7$$ Find the a) Jordan canonical form of ##A## b) characteristic polynomial c) minimal polynomial d) ##dim\,kerA## When: case 1: we know that ##A## is...

Homework Statement Let T: ℝ² → P² a linear transformation with usual operations such as T [1 1] = 1 - 2x and T [3 -1]= x+2x² Find T [-7 9] and T [a b] **Though I'm writing them here as 1x 2 row vectors , all T's are actually 2x1 column vectors (I didn't see a way to give them proper...

I posted this elsewhere and was sort of able to figure out a result myself, but 1) I didn't do it right, and 2) No one answered it anyway. I thought I'd give it a shot over here. The problem deals with nested matrices. The gamma matrices can be found here. My question deals with a "vector"...

##\begin{align}[A(BC)]_{ij} &= \sum_r A_{ir}(BC)_{rj} \\ &= \sum_r A_{ir} \sum_s B_{rs}C_{sj}\\ &= \sum_r\sum_s A_{ir}B_{rs}C_{sj}\\ &= \sum_{s} (\sum_{r} A_{ir} B_{rs}) C_{sj} \\ &= [(AB) C]_{ij}\end{align}## How did it went from ##2## to ##3##. In general is there a proof that sums can be...

If ##A## is ##m \times n## matrix, ##B## is an ##n \times m## matrix and ##n < m##. Then show that ##AB## is not invertible. Let ##R## be the reduced echelon form of ##AB## and let ##AB## be invertible. ##I = P(AB)## where ##P## is some invertible matrix. Since ##n < m## and ##B## is ##n...

Homework Statement Let ##A## be an ##m \times n## matrix. Show that by means of a finite number of elementary row/column operations ##A## can be reduced to both "row reduced echelon" and "column reduced echelon" matrix ##R##. i.e ##R_{ij} = 0## if ##i \ne j##, ##R_{ii} = 1 ##, ##1 \le i \le...

Homework Statement Find the inverse of ##A = \begin{bmatrix} 1 & \dfrac12 & & \cdots && \dfrac1n \\\dfrac12 & \dfrac13 && \cdots && \dfrac1{n+1} \\ \vdots & \vdots && && \vdots \\ \dfrac1n & \dfrac1{n+1} && \cdots && \dfrac1{2n-1}\end{bmatrix}## Homework EquationsThe Attempt at a SolutionI...

Hello friends, I'm trying to construct transformation matrix S such that it transforms Dirac representations of gamma matrices into Chiral ones. I know that this S should be hermitian and unitary and from this I arrived an equation with 2 matrices on the LHS (a known matrix multiplied by S from...

Prove that interchange of two rows of a matrix can be accomplished by a finite sequence of elemenatary row operations of the other two types. My proof :- If ##A_k## is to be interchanged by ##A_l## then, ##\displaystyle \begin{align} A_k &\to A_l + A_k \\ A_l &\to - A_l \\ A_l &\to A_k + A_l...

Hello, if I have some given vector c \in R^n, then I want to find solutions X \in R^{n\times n} to the following equation: X C X^T = C where C = c c^T. Certainly X = I is a solution, but I'm looking for any nontrivial solutions. We can also assume X is invertible if that helps. This equation...

I got an image called img and I want to sharpen the vertical spatial lines. I created this matrix: hp = [-3 -2 -1 12 -1 -2 -3]; hp= rot90(h_lowp); Then I do this to get the new image: newimg = uint8(conv2(single(hp), single(img))); It SORTA works, but I'm not so sure why it works. I mean all...